Mathematical Fluid Mechanics, 2001 Recent Results and Open Questions Advances in Mathematical Fluid Mechanics Series

Mathematical modeling and numerical simulation in fluid mechanics are topics of great importance both in theory and technical applications. The present book attempts to describe the current status in various areas of research. The 10 chapters, mostly survey articles, are written by internationally renowned specialists and offer a range of approaches to and views of the essential questions and problems. In particular, the theories of incompressible and compressible Navier-Stokes equations are considered, as well as stability theory and numerical methods in fluid mechanics. Although the book is primarily written for researchers in the field, it will also serve as a valuable source of information to graduate students.

What Use for the Mathematical Theory of the Navier-Stokes Equations.- An Iterative Scheme for Steady Compressible Viscous Flow, Modified to Treat Large Potential Forces.- Raviart: Asymptotic Results for the Linear Stage of the Rayleigh Taylor Instability.- Recent Progress in the Mathematical Theory of Viscous Compressible Fluids.- Numerical Methods for Compressible Flow.- Instability of Steady Flows of an Ideal Incompressible Fluid.- Finite Volume Solution of 2D and 3D Euler and Navier-Stokes Equations.- On a Conjecture Concerning the Stokes Problem in Nonsmooth Domains.- On Well-Posedness of the Navier-Stokes Equations.- Anisotropie and Geometric Criteria for Interior Regularity of Weak Solutions to the 3D Navier-Stokes Equations.- List of Authors.