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)

Most of the scientific interest in incompressible fluid dynamics is, in one way or another, associated with the dynamics of small scales. In particular, the generation and amplification of small-scale motions is at the heart of the analysis of instabilities, of the problem of finite-time singularities, of fluid-structure interaction and of the study of both onset and fully developed turbulence. This topic has a long history and remains very active today. As the mathematical toolbox increases and with the improvement of high-speed computing, it has seen considerable progress in recent years. In this workshop we will focus on exploring this point-of-view while showcasing recent results and encouraging new collaborations.

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.

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.