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... (more)

This conference will explore several themes: (a) physical and computer experiments on the formation of singularities in fluids through state-of-the-art simulations and high speed, high resolution imaging of droplets, filaments, jets, splashes, jumps, and vortical structures, and (b) the development of theoretical models for the analysis of such phenomena. Our principal goal is to stimulate the interaction between analysts, modellers and experimentalists in the area, especially since much of the experimental work remains to be explained.

Water wave problems often require specific computational tools, and computations often inform the search for theoretical results. This workshop will bring both of these aspects together. Topics to be discussed include methods and results for steady and unsteady waves, including boundary integral, conformal maps and Euler truncations, with applications to capillary, gravity, flexural, vortical, electro-hydrodynamic, and geophysical waves. Computational questions in water waves have inspired research for over 60 years. In particular, the conference will celebrate the work of Jean-Marc Vanden-Broeck, who has been making important contributions in the field since the 1970s.

The theory of water waves has been at the forefront of mathematics for over two centuries. In recent years there has been an explosion of interest in the subject. This workshop will bring together researchers contributing to all aspects of water waves: experiments, computation and analysis. Currently active topics in water waves include the effects of viscosity, surface tension, vorticity, surface wind and bottom topography on both time-dependent and steady waves. However, the workshop will range well beyond these topics.