Incompressible fluids are an abundant source of mathematical and practical problems. The question of global-in-time regularity versus finite-time singularity formation for incompressible fluids, governed by the Navier-Stokes or Euler equations, has been one of the most challenging outstanding problems in applied PDE. There have also been new developments in the study of the onset of turbulence due to linear and nonlinear instabilities in incompressible fluids. Interfacial and surface water waves are physical phenomena that, in addition to the challenges outlined above, involve the evolution of free boundaries. These problems embody many of the mathematical challenges found in studies of nonlinear PDEs.
Progress on these topics is possible because of advances in analysis, numerical computations and physical experiments. In addition, ocean field observations provide a reality test to all conclusions and invite new problems to be addressed. In this program, we provide a venue for interaction among researchers engaged in all of these problem-solving techniques to focus on topics arising in incompressible fluids.
Topics of particular interest include: singularity formation, stability and bifurcation; the modeling and analysis of simplified phenomenological models for the description of coherent structures; and time-dependent and steady free boundary problems including water waves, vortex sheets, capillary problems with contact lines and viscous waves with boundary layers.
Image courtesy of Dr. Véronique Sarano. All further use is prohibited without the express permission of Dr. Sarano.
Claude Bardos, Edriss S. Titi, Onsager’s Conjecture for the Incompressible Euler Equations in Bounded Domains, Archive for Rational Mechanics and Analysis 228 (2017) no. 1, 197–207.
Noah Stevenson, Ian Tice, Traveling Wave Solutions to the Multilayer Free Boundary Incompressible Navier--Stokes Equations, SIAM Journal on Mathematical Analysis 53 (2021) no. 6, 6370-6423.
Jon Wilkening, Traveling-standing water waves, Fluids 6 (2021) no. 5, 187.
Natalia Sannikova, Diego Arcas, Harvey Segur, Tsunami amplitude decay on source aspect ratio investigation, AGU Fall Meeting Abstracts, vol. 2020, 2020, pp. NH014-0028.
Bosco Garc{\'\i}a-Archilla, Julia Novo, Edriss S Titi, Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier--Stokes Equations, SIAM Journal on Numerical Analysis 58 (2020) no. 1, 410-429.
Dragos Iftimie, Milton C Lopes Filho, HJ Nussenzveig Lopes, Weak vorticity formulation of the incompressible 2D Euler equations in bounded domains, Communications in Partial Differential Equations 45 (2020) no. 2, 109-145.
Elaine Cozzi, James P Kelliher, Well-posedness of the 2D Euler equations when velocity grows at infinity, arXiv preprint arXiv:1709.07422 (2017).
Harvey Segur, Soroush Khadem, Wind-Driven Waves on the Air-Water Interface, Fluids 6 (2021), 122.
Katie L Oliveras, Salvatore Calatola-Young, A different derivation of conservation laws for water waves, arXiv preprint arXiv:2105.07580 (2021).
James Wing Chee Graham, Katie L Oliveras, Olga Trichtchenko, A Novel Method for Generating 3D Hydrodynamic Conservation Laws, arXiv preprint arXiv:2111.15558 (2021).
Huy Q Nguyen, Beno{\^\i}t Pausader, A paradifferential approach for well-posedness of the Muskat problem, Archive for Rational Mechanics and Analysis 237 (2020) no. 1, 35-100.
KL Oliveras, A Weak Formulation of Water Waves in Surface Variables, arXiv preprint arXiv:2008.00940 (2020).
Claude Bardos, Nicolas Besse, About the derivation of the quasilinear approximation in plasma physics, arXiv preprint arXiv:2011.08085 (2020).
Qing Li, Baylor Fox-Kemper, Anisotropy of Langmuir turbulence and the Langmuir-enhanced mixed layer entrainment, Physical Review Fluids 5 (2020) no. 1, 013803.
Claude W Bardos, Edriss S Titi, C 0, $\alpha$ boundary regularity for the pressure in weak solutions of the 2 d Euler equations, Philosophical Transactions of the Royal Society A 380 (2022) no. 2218, 20210073.
Carlos A Galeano-Rios, Radu Cimpeanu, Isabelle A Bauman, Annika MacEwen, Paul A Milewski, Daniel M Harris, Capillary-scale solid rebounds: experiments, modelling and simulations, Journal of Fluid Mechanics 912 (2021).
E Grenier, Derivation of the ion equation, Quarterly of applied mathematics 78 (2020) no. 2.
Claude Bardos, Nicolas Besse, Diffusion limit of the Vlasov equation in the weak turbulent regime, Journal of Mathematical Physics 62 (2021) no. 10, 101505.
Julien Guillod, Mikhail Korobkov, Xiao Ren, Existence and uniqueness for plane stationary Navier-Stokes flows with compactly supported force, arXiv preprint arXiv:2111.11042 (2021).
Juhi Jang, Walter A Strauss, Yilun Wu, Existence of Rotating Stars with Variable Entropy, arXiv preprint arXiv:2111.04634 (2021).
Matthew Durey, Paul A Milewski, Zhan Wang, Faraday pilot-wave dynamics in a circular corral, Journal of Fluid Mechanics 891 (2020).
AI Dyachenko, SA Dyachenko, VE Zakharov, Free Surface in 2D Potential Flow: Singularities, Invariants and Virtual Fluid, arXiv preprint arXiv:2109.13159 (2021).
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, From hard spheres dynamics to the Stokes--Fourier equations: an L2 analysis of the Boltzmann--Grad limit, Comptes Rendus Mathematique 353 (2015) no. 7, 623-627.
Yan Guo, Benoit Pausader, Klaus Widmayer, Global Axisymmetric Euler Flows with Rotation, arXiv preprint arXiv:2109.01029 (2021).
Walter A Strauss, Yilun Wu, Global Continuation of a Vlasov Model of Rotating Galaxies, arXiv preprint arXiv:2203.01454 (2022).
Dongfen Bian, Xueke Pu, Global smooth axisymmetic solutions of the Boussinesq equations for magnetohydrodynamics convection, Journal of Mathematical Fluid Mechanics 22 (2020) no. 1, 1-13.
David M Ambrose, Anna L Mazzucato, Global Solutions of the Two-Dimensional Kuramoto--Sivashinsky Equation with a Linearly Growing Mode in Each Direction, Journal of Nonlinear Science 31 (2021) no. 6, 1-26.
Hongjie Dong, Francisco Gancedo, Huy Q Nguyen, Global well-posedness for the one-phase Muskat problem, arXiv preprint arXiv:2103.02656 (2021).
Dongfen Bian, Yao Xiao, Global well-posedness of non-isothermal inhomogeneous nematic liquid crystal flows, Discrete \& Continuous Dynamical Systems-B 26 (2021) no. 3, 1243.
Jongkeun Choi, Hongjie Dong, Longjuan Xu, Gradient estimates for Stokes and Navier-Stokes systems with piecewise DMO coefficients, arXiv preprint arXiv:2105.05429 (2021).
Jon Wilkening, Harmonic stability of standing water waves, arXiv preprint arXiv:1903.05621 (2019).
Ryan Creedon, Bernard Deconinck, Olga Trichtchenko, High-frequency instabilities of a Boussinesq--Whitham system: a perturbative approach, Fluids 6 (2021) no. 4, 136.
Ryan P Creedon, Bernard Deconinck, Olga Trichtchenko, High-frequency instabilities of Stokes waves, Journal of Fluid Mechanics 937 (2022).
Ryan Creedon, Bernard Deconinck, Olga Trichtchenko, High-frequency instabilities of the Kawahara equation: a perturbative approach, SIAM Journal on Applied Dynamical Systems 20 (2021) no. 3, 1571-1595.
Natalia K Sannikova, Harvey Segur, Diego Arcas, Influence of Tsunami Aspect Ratio on Near and Far-Field Tsunami Amplitude, Geosciences 11 (2021) no. 4, 178.
Ruben J Tomlin, Radu Cimpeanu, Demetrios T Papageorgiou, Instability and dripping of electrified liquid films flowing down inverted substrates, Physical Review Fluids 5 (2020) no. 1, 013703.
Hongjie Dong, Yan Guo, Timur Yastrzhembskiy, Kinetic Fokker-Planck and Landau equations with specular reflection boundary condition, arXiv preprint arXiv:2111.09840 (2021).
Qiming Wang, Demetrios T Papageorgiou, Jean-Marc Vanden-Broeck, Korteweg--de Vries solitons on electrified liquid jets, Physical Review E 91 (2015) no. 6, 063012.
Adrian Constantin, Walter Strauss, Eugen V{\u{a}}rv{\u{a}}ruc{\u{a}}, Large-amplitude steady downstream water waves, Communications in Mathematical Physics 387 (2021) no. 1, 237-266.
Dongfen Bian, Yan Guo, Ian Tice, Linear instability of Z-pinch in plasma: Inviscid case, Mathematical Models and Methods in Applied Sciences 31 (2021) no. 02, 409-472.
Dongfen Bian, Yan Guo, Ian Tice, Linear instability of Z-pinch in plasma: Viscous case, Mathematical Models and Methods in Applied Sciences 30 (2020) no. 14, 2827-2908.
Demetrios T Papageorgiou, Saleh Tanveer, Mathematical study of a system of multi-dimensional non-local evolution equations describing surfactant-laden two-fluid shear flows, Proceedings of the Royal Society A 477 (2021) no. 2252, 20210307.
Hannah Potgieter, John D Carter, Diane M Henderson, Modeling the Second Harmonic in Surface Water Waves Using Generalizations of NLS, Water Waves (2022), 1-25.
Jinbing Chen, Dmitry E Pelinovsky, Jeremy Upsal, Modulational instability of periodic standing waves in the derivative NLS equation, Journal of Nonlinear Science 31 (2021) no. 3, 1-32.
Tianwen Luo, Edriss S Titi, Non-uniqueness of weak solutions to hyperviscous Navier--Stokes equations: on sharpness of J.-L. Lions exponent, Calculus of Variations and Partial Differential Equations 59 (2020) no. 3, 1-15.
Antoine Remond-Tiedrez, Nonlinear Partial Differential Equations in Fluid Dynamics: Interfaces, Microstructure, and Stability, Ph.D. thesis, Carnegie Mellon University, 2020.
David M Ambrose, Roberto Camassa, Jeremy L Marzuola, Richard M McLaughlin, Quentin Robinson, Jon Wilkening, Numerical Algorithms for Water Waves with Background Flow over Obstacles and Topography, arXiv preprint arXiv:2108.01786 (2021).
Kazuki Koga, Numerical reparametrization of periodic planar curves via curvature interpolation, arXiv preprint arXiv:2110.12432 (2021).
Benoit Pausader, Yan Guo, Klaus Widmayer, On long time existence for small solutions to Euler-Coriolis, 2021 Spring Eastern Virtual Sectional Meeting, AMS, 2021.
Sergey A Dyachenko, On the dynamics of a free surface of an ideal fluid in a bounded domain in the presence of surface tension, Journal of Fluid Mechanics 860 (2019), 408-418.
Claude Bardos, Piotr Gwiazda, Agnieszka {\'S}wierczewska-Gwiazda, Edriss S Titi, Emil Wiedemann, On the extension of Onsager’s conjecture for general conservation laws, Journal of Nonlinear Science 29 (2019) no. 2, 501-510.
Dongfen Bian, On the nonlinear stability and instability of the Boussinesq system for magnetohydrodynamics convection, Mathematics 8 (2020) no. 7, 1049.
Kristoffer Varholm, Erik Wahl{\'e}n, Samuel Walsh, On the stability of solitary water waves with a point vortex, Communications on Pure and Applied Mathematics 73 (2020) no. 12, 2634-2684.
Yan Guo, Chunyan Huang, Benoit Pausader, Klaus Widmayer, On the stabilizing effect of rotation in the 3d Euler equations, arXiv preprint arXiv:2010.10460 (2020).
Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond, Sergio Simonella, One-sided convergence in the Boltzmann-Grad limit, arXiv preprint arXiv:1612.03722 (2016).
Huy Q Nguyen, Walter A Strauss, Proof of modulational instability of Stokes waves in deep water, arXiv preprint arXiv:2007.05018 (2020).
Hantaek Bae, James P Kelliher, Propagation of striated regularity of velocity for the Euler equations, arXiv preprint arXiv:1508.01915 24 (2015).
Jon Wilkening, Xinyu Zhao, Quasi-periodic travelling gravity--capillary waves, Journal of Fluid Mechanics 915 (2021).
Walter A. Strauss, Yilun Wu, Rapidly Rotating Stars, Communications in Mathematical Physics 368 (2019) no. 2, 701-721.
Jeremy Upsal, Bernard Deconinck, Real Lax spectrum implies spectral stability, Studies in Applied Mathematics 145 (2020) no. 4, 765-790.
Joseph Skitka, JB Marston, Baylor Fox-Kemper, Reduced-order quasilinear model of ocean boundary-layer turbulence, Journal of Physical Oceanography 50 (2020) no. 3, 537-558.
Dallas Albritton, Hongjie Dong, Regularity properties of passive scalars with rough divergence-free drifts, arXiv preprint arXiv:2107.12511 (2021).
CH Aurther, Rafael Granero-Belinch{\'o}n, Steve Shkoller, Jon Wilkening, Rigorous asymptotic models of water waves, Water Waves 1 (2019) no. 1, 71-130.
Eduardo Garc{\'\i}a-Ju{\'a}rez, Javier G{\'o}mez-Serrano, Huy Q Nguyen, Beno{\^\i}t Pausader, Self-similar solutions for the Muskat equation, Advances in Mathematics 399 (2022), 108294.
Kazuki Koga, Signal processing approach to mesh refinement in simulations of axisymmetric droplet dynamics, Journal of Computational and Applied Mathematics 383 (2021), 113131.
Jon Wilkening, Xinyu Zhao, Spatially quasi-periodic water waves of infinite depth, Journal of Nonlinear Science 31 (2021) no. 3, 1-43.
Yan Guo, Ian Tice, Stability of contact lines in fluids: 2D Navier-Stokes flow, arXiv preprint arXiv:2010.15713 (2020).
Dongfen Bian, Shouyi Dai, Jingjing Mao, Stability of Couette flow for 2D Boussinesq system in a uniform magnetic field with vertical dissipation, Applied Mathematics Letters 121 (2021), 107415.
Emmanuel Grenier, Toan T. Nguyen, Stability of shear flows near a boundary, 2020.
Jeremy Upsal, Stability of solutions of integrable partial differential equations, University of Washington, 2020.
Dongfen Bian, Xueke Pu, Stability threshold for 2D shear flows of the Boussinesq system near Couette, arXiv preprint arXiv:2012.02386 (2020).
Sergey A Dyachenko, Vera Mikyoung Hur, Stokes waves with constant vorticity: I. Numerical computation, Studies in Applied Mathematics 142 (2019) no. 2, 162-189.
Sergey A Dyachenko, Vera Mikyoung Hur, Stokes waves with constant vorticity: folds, gaps and fluid bubbles, Journal of Fluid Mechanics 878 (2019), 502-521.
Claude Bardos, Trinh T Nguyen, Toan T Nguyen, Edriss S Titi, The inviscid limit for the $2 d $ Navier-Stokes equations in bounded domains, arXiv preprint arXiv:2111.14782 (2021).
Erik Van Sebille, Stefano Aliani, Kara Lavender Law, Nikolai Maximenko, Jos{\'e} M Alsina, Andrei Bagaev, Melanie Bergmann, Bertrand Chapron, Irina Chubarenko, Andr{\'e}s C{\'o}zar, others, The physical oceanography of the transport of floating marine debris, Environmental Research Letters 15 (2020) no. 2, 023003.
Saad Qadeer, Ehssan Nazockdast, Boyce E Griffith, The Projection Extension Method: A Spectrally Accurate Technique for Complex Domains, arXiv preprint arXiv:2111.07944 (2021).
Saad Qadeer, Boyce E Griffith, The smooth forcing extension method: A high-order technique for solving elliptic equations on complex domains, Journal of Computational Physics 439 (2021), 110390.
Hongjie Dong, Yan Guo, Zhimeng Ouyang, The Vlasov-Poisson-Landau system with the specular-reflection boundary condition, arXiv preprint arXiv:2010.05314 (2020).
Hongjie Dong, Chulan Zeng, Qi S Zhang, Time analyticity for fractional heat equations, arXiv preprint arXiv:2108.01128 (2021).
Hongjie Dong, Xinghong Pan, Time Analyticity for Inhomogeneous Parabolic Equations and the Navier--Stokes Equations in the Half Space, Journal of Mathematical Fluid Mechanics 22 (2020) no. 4, 1-20.
Sergey A Dyachenko, Traveling capillary waves on the boundary of a disc, arXiv preprint arXiv:1911.07557 (2019).
Susanna Haziot, Vera Hur, Walter Strauss, John Toland, Erik Wahl{\'e}n, Samuel Walsh, Miles Wheeler, Traveling water waves—the ebb and flow of two centuries, Quarterly of Applied Mathematics 80 (2022) no. 2, 317-401.
Giovanni Leoni, Ian Tice, Traveling wave solutions to the free boundary incompressible Navier-Stokes equations, arXiv preprint arXiv:1912.10091 (2019).
Jeffrey Knowles, Harry Yeh, Fourfold amplification of solitary-wave Mach reflection at a vertical wall, Journal of Fluid Mechanics 861 (2019), 517–523.
Olga Trichtchenko, Bernard Deconinck, Richard Koll{\'a}r, Stability of Periodic Traveling Wave Solutions to the Kawahara Equation, SIAM J. Appl. Dyn. Syst. 17 (2018), 2761-2783.
Qing Li, Baylor Fox-Kemper, Oyvind Breivik, Adrean Webb, Statistical Models of Global Langmuir Mixing, Ocean Modelling 113 (2017).
Walter A. Strauss, Yilun Wu, Steady States of Rotating Stars and Galaxies, SIAM J. Math. Anal. 49 (2017), 4865-4914.
Emmanuel Grenier, Toan T. Nguyen, Sublayer of Prandtl Boundary Layers, Archive for Rational Mechanics and Analysis 229 (2018) no. 3, 1139–1151.
Toan T. Nguyen, Trinh T. Nguyen, The Inviscid Limit of Navier–Stokes Equations for Analytic Data on the Half-Space, Archive for Rational Mechanics and Analysis 230 (2018) no. 3, 1103–1129.
Quansen Jiu, Milton C. Lopes Filho, Dongjuan Niu, Helena J. Nussenzveig Lopes, The limit of vanishing viscosity for the incompressible 3D Navier–Stokes equations with helical symmetry, Physica D: Nonlinear Phenomena 376-377 (2018), 238–246.
Bernard Deconinck, Jeremy Upsal, The Orbital Stability of Elliptic Solutions of the Focusing Nonlinear Schr\"odinger Equation, SIAM J. Math. Anal. 52 (2020), 1-41.
Gung-Min Gie, James P. Kelliher, Milton C. Lopes Filho, Anna L. Mazzucato, Helena J. Nussenzveig Lopes, The vanishing viscosity limit for some symmetric flows, Annales de l'Institut Henri Poincar{\'e} C, Analyse non lin{\'e}aire (2019).
Antoine Remond-tiedrez, Ian Tice, The Viscous Surface Wave Problem with Generalized Surface Energies, SIAM J. Math. Anal. 51 (2019), 4894-4952.
P. M. Lushnikov, N. Vladimirova, Toward Defeating Diffraction and Randomness for Laser Beam Propagation in Turbulent Atmosphere, JETP Letters 108 (2018) no. 9, 571–576.
André Nachbin, Paul Milewski, John Bush, Tunneling with a hydrodynamic pilot-wave model, Physical Review Fluids 2 (2017), 034801.
David Andrade Perez, André Nachbin, Two-Dimensional Surface Wave Propagation over Arbitrary Ridge-Like Topographies, SIAM Journal on Applied Mathematics 78 (2018), 2465-2490.
Seung Wook So, Walter A. Strauss, Upper bound on the slope of steady water waves with small adverse vorticity, Journal of Differential Equations 264 (2018) no. 6, 4136-4151.
Peter Constantin, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes, Vlad Vicol, Vorticity Measures and the Inviscid Limit, Archive for Rational Mechanics and Analysis 234 (2019) no. 2, 575–593.
André Nachbin, Walking droplets correlated at a distance, Chaos: An Interdisciplinary Journal of Nonlinear Science 28 (2018) no. 9, 096110.
Yue Pu, Robert L. Pego, Denys Dutykh, Didier Clamond, Weakly singular shock profiles for a non-dispersive regularization of shallow-water equations, Communications in Mathematical Sciences 16 (2018) no. 5, 1361–1378.
Olga Trichtchenko, Paul A. Milewski, Emilian I. Părău, Jean-Marc Vanden-Broeck, Stability of Periodic Travelling Flexural-Gravity Waves in Two Dimensions, arXiv 1801.09748 (2018).
Qing Li, Baylor Fox-Kemper, Assessing the Effects of Langmuir Turbulence on the Entrainment Buoyancy Flux in the Ocean Surface Boundary Layer, Journal of Physical Oceanography 47 (2017).
Ian Tice, Asymptotic stability of shear-flow solutions to incompressible viscous free boundary problems with and without surface tension, Zeitschrift für angewandte Mathematik und Physik 69 (2018) no. 2.
Gung-Min Gie, James Kelliher, A. Mazzucato, Boundary Layers for the Navier–Stokes Equations Linearized Around a Stationary Euler Flow, Journal of Mathematical Fluid Mechanics 20 (2018), 1-22.
André Nachbin, Roberto Ribeiro, Capturing the flow beneath water waves, Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences 376 (2018), 20170098.
Saad Qadeer, Jon Wilkening, Computing the Dirichlet-Neumann Operator on a Cylinder, SIAM J. Numer. Anal. 57 (2019), 1183-1204.
David M. Ambrose, Milton C. Lopes Filho, Helena J. Nussenzveig Lopes, Confinement of vorticity for the 2D Euler-$\alpha$ equations, Journal of Differential Equations (2018).
Animikh Biswas, Ciprian Foias, Cecilia F. Mondaini, Edriss S. Titi, Downscaling data assimilation algorithm with applications to statistical solutions of the Navier–Stokes equations, Annales de l'Institut Henri Poincar{\'e} C, Analyse non lin{\'e}aire (2019).
Ian Tice, Lei Wu, Dynamics and Stability of Surface Waves with Bulk-Soluble Surfactants, Acta Applicandae Mathematicae 161 (2017), 35-70.
A. I. Dyachenko, S. A. Dyachenko, P. M. Lushnikov, V. E. Zakharov, Dynamics of poles in two-dimensional hydrodynamics with free surface: new constants of motion, Journal of Fluid Mechanics 874 (2019), 891–925.
Alexey Cheskidov, Milton Lopes Filho, Helena Nussenzveig Lopes, Roman Shvydkoy, Energy Conservation in Two-dimensional Incompressible Ideal Fluids, Communications in Mathematical Physics 348 (2016).
Pavel M. Lushnikov, Nikolay M. Zubarev, Exact Solutions for Nonlinear Development of a Kelvin-Helmholtz Instability for the Counterflow of Superfluid and Normal Components of Helium II, Physical Review Letters 120 (2018) no. 20.
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler, Existence and qualitative theory for stratified solitary water waves, Annales de l’Institut Henri Poincaré C, Analyse non linéaire 35 (2018) no. 2, 517–576.
Julien Guillod, Peter Wittwer, Existence and uniqueness of steady weak solutions to the Navier–Stokes equations in ℝ², Proceedings of the American Mathematical Society 146 (2018) no. 10, 4429–4445.
Juhi Jang, Walter Strauss, Yilun Wu, Existence of rotating magnetic stars, Physica D: Nonlinear Phenomena 397 (2019), 65-74.
Robin Ming Chen, Samuel Walsh, Miles H. Wheeler, Existence, Nonexistence, and Asymptotics of Deep Water Solitary Waves with Localized Vorticity, Archive for Rational Mechanics and Analysis 234 (2019) no. 2, 595–633.
Alexei A. Mailybaev, Andr{\'e} Nachbin, Explosive ripple instability due to incipient wave breaking, Journal of Fluid Mechanics 863 (2019), 876 - 892.
Roberto Ribeiro, Paul Milewski, André Nachbin, Flow structure beneath rotational water waves with stagnation points, Journal of Fluid Mechanics 812 (2017), 792-814.
Bernard Deconinck, Qi Guo, Eli Shlizerman, Vishal Vasan, Fokas’s Unified Transform Method for linear systems, Quarterly of Applied Mathematics 76 (2017), 1.
David M. Ambrose, Anna L. Mazzucato, Global Existence and Analyticity for the 2D Kuramoto–Sivashinsky Equation, Journal of Dynamics and Differential Equations 31 (2017), 1525-1547.
Emmanuel Grenier, Toan T. Nguyen, Green Function of Orr-Sommerfeld Equations Away from Critical Layers, SIAM J. Math. Anal. 51 (2019), 1279-1296.
Denis A. Silantyev, Pavel M. Lushnikov, Harvey A. Rose, Langmuir wave filamentation in the kinetic regime. I. Filamentation instability of Bernstein-Greene-Kruskal modes in multidimensional Vlasov simulations, Physics of Plasmas 24 (2017) no. 4, 042104.
Denis A. Silantyev, Pavel M. Lushnikov, Harvey A. Rose, Langmuir wave filamentation in the kinetic regime. II. Weak and strong pumping of nonlinear electron plasma waves as the route to filamentation, Physics of Plasmas 24 (2017) no. 4, 042105.
Logan G. Wright, Zachary M. Ziegler, Pavel M. Lushnikov, Zimu Zhu, M. Amin Eftekhar, Demetrios N. Christodoulides, Frank W. Wise, Multimode Nonlinear Fiber Optics: Massively Parallel Numerical Solver, Tutorial, and Outlook, IEEE Journal of Selected Topics in Quantum Electronics 24 (2018) no. 3, 1–16.
Pavel M. Lushnikov, Sergey A. Dyachenko, Denis A. Silantyev, New conformal mapping for adaptive resolving of the complex singularities of Stokes wave, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473 (2017) no. 2202, 20170198.
A. I. Dyachenko, P. M. Lushnikov, V. E. Zakharov, Non-canonical Hamiltonian structure and Poisson bracket for two-dimensional hydrodynamics with free surface, Journal of Fluid Mechanics 869 (2019), 526–552.
Ruben Tomlin, Anna Kalogirou, Demetrios Papageorgiou, Nonlinear dynamics of a dispersive anisotropic Kuramoto--Sivashinsky equation in two space dimensions, Proceedings of The Royal Society A 474 (2018).
Prasun Ray, Jordan Hauge, Demetrios Papageorgiou, Nonlinear interfacial instability in two-fluid viscoelastic Couette flow, Journal of Non-Newtonian Fluid Mechanics 251 (2017).
Julien Guillod, Guido Schneider, Peter Wittwer, Dominik Zimmermann, Nonlinear Stability at the Eckhaus Boundary, SIAM Journal on Mathematical Analysis 50 (2018) no. 5, 4699–4720.
Evangelos Papaefthymiou, Demetrios Papageorgiou, Nonlinear stability in three-layer channel flows, Journal of Fluid Mechanics 829 (2017).
Tao Gao, Jean-Marc Vanden-Broeck, Zhan Wang, Numerical computations of two-dimensional flexural-gravity solitary waves on water of arbitrary depth, IMA Journal of Applied Mathematics 83 (2018).
Jeffrey Knowles, Harry Yeh, On shoaling of solitary waves, Journal of Fluid Mechanics 848 (2018), 1073–1097.
Bernard Deconinck, Jeremy Upsal, On the nonintegrability of equations for long- and short-wave interactions, Physics Letters A 382 (2018) no. 29, 1916–1921.
Claude Bardos, Edriss S. Titi, Onsager’s Conjecture for the Incompressible Euler Equations in Bounded Domains, Archive for Rational Mechanics and Analysis 228 (2017) no. 1, 197–207.
Claude Bardos, Piotr Gwiazda, Agnieszka Świerczewska-Gwiazda, Edriss S. Titi, Emil Wiedemann, Onsager's conjecture in bounded domains for the conservation of entropy and other companion laws, Proceedings of the Royal Society A 475 (2019).
Claude Bardos, Edriss S. Titi, Emil Wiedemann, Onsager’s Conjecture with Physical Boundaries and an Application to the Vanishing Viscosity Limit, Communications in Mathematical Physics 370 (2019) no. 1, 291–310.
Robin Ming Chen, Cheng Yu, Onsager's energy conservation for inhomogeneous Euler equations, Journal de Math{\'e}matiques Pures et Appliqu{\'e}es (2019).
Didier Clamond, Remarks on Bernoulli constants, gauge conditions and phase velocities in the context of water waves, Appl. Math. Lett. 74 (2017), 114-120.
Marcelo Flamarion, Paul Milewski, André Nachbin, Rotational waves generated by current-topography interaction, Studies in Applied Mathematics 142 (2019).
Olga Trichtchenko, Emilian I. Părău, Jean-Marc Vanden-Broeck, Paul Milewski, Solitary flexural\&\#x2013;gravity waves in three dimensions, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376 (2018) no. 2129, 20170345.
Adelaide Akers, Samuel Walsh, Solitary water waves with discontinuous vorticity, Journal de Mathématiques Pures et Appliquées 124 (2019), 220–272.
John D. Carter, Bidirectional Whitham Equations as Models of Waves on Shallow Water., arXiv 1705.06503 (2017).
Xuecheng Wang, Decay estimates for the \$3D\$ relativistic and non-relativistic Vlasov-Poisson systems, arXiv 1805.10837 (2018).
Ian Tice, Samuel Zbarsky, Decay of Solutions to the Linearized Free Surface Navier–Stokes Equations with Fractional Boundary Operators, arXiv 1806.04056 (2018).
Emmanuel Grenier, Toan T. Nguyen, Green function for linearized Navier-Stokes around a boundary layer profile: near critical layers, arXiv 1705.05323 (2017).
Emmanuel Grenier, Toan T. Nguyen, \$\$L^\infty \$\$ Instability of Prandtl Layers, arXiv: 1803.11024 (2018).
Emmanuel Grenier, Toan T. Nguyen, Frederic Rousset, Avy Soffer, Linear inviscid damping and enhanced viscous dissipation of shear flows by using the conjugate operator method, arXiv 1804.08291 (2018).
Julien Guillod, Vladim'ir vSver'ak, Numerical investigations of non-uniqueness for the Navier-Stokes initial value problem in borderline spaces, arXiv 1704.00560 (2017).
Emmanuel Grenier, Toan T. Nguyen, On nonlinear instability of Prandtl's boundary layers: the case of Rayleigh's stable shear flows, arXiv 1706.01282 (2017).
Kristoffer Varholm, Erik Wahl'en, Samuel Walsh, On the Stability of Solitary Water Waves with a Point Vortex, arXiv 1811.08024 (2018).
Xuecheng Wang, Propagation of Regularity and Long Time Behavior of 3D Massive Relativistic Transport Equation I: Vlasov–Nordstr\"om System, arXiv 1804.06560 (2018).
Xuecheng Wang, Propagation of regularity and long time behavior of the \$3D\$ massive relativistic transport equation II: Vlasov-Maxwell system, arXiv 1804.06566 (2018).
Emmanuel Grenier, Toan Nguyen, Sharp bounds on linear semigroup of Navier Stokes with boundary layer norms, Journal of Differential Equations (2017).
John D. Carter, Diane Henderson, Isabelle Butterfield, A comparison of frequency downshift models of wave trains on deep water, Physics of Fluids 31 (2019) no. 1, 013103.
Vishal Vasan, Katie Oliveras, Diane Henderson, Bernard Deconinck, A method to recover water-wave profiles from pressure measurements, Wave Motion 75 (2017), 25-35.
D. Andrade, A. Nachbin, A three-dimensional Dirichlet-to-Neumann operator for water waves over topography, Journal of Fluid Mechanics 845 (2018), 321–345.
