Mathematical Aspects of Hydrodynamics

Abstract

The workshop was devoted to discussions of recent developments and possible future directions of research in the field of mathematical hydrodynamics. Many of the leading experts in the theory of PDE’s arising in fluid dynamics participated in this event. The topics included:

• Regularity, uniqueness and well-posedness problems for the NavierStokes equations
• Stability of Navier-Stokes solutions
• Open problems concerning the steady-state Navier-Stokes solutions
• Statistical approach to 2d hydrodynamics
• Inviscid limits of Navier-Stokes solutions
• Anomalous weak solutions of Euler’s equation
• Finding physically reasonable classes of weak solutions of Euler’s equations
• Local well-posedness of Euler’s equations in optimal spaces
• Stability of solutions of Euler’s equations
• Water waves
• Model equations
• Geometric approach to hydromechanical equations
• Selected compressible flow problems Mathematics