Mathematical Fluid Mechanics
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...
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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.
ForewordWhat Use for the Mathematical Theory of the Navier-Stokes Equations1An Iterative Scheme for Steady Compressible Viscous Flow, Modified to Treat Large Potential Forces27Asymptotic Results for the Linear Stage of the Rayleigh-Taylor Instability47Recent Progress in the Mathematical Theory of Viscous Compressible Fluids73Numerical Methods for Compressible Flow105Instability of Steady Flows of an Ideal Incompressible Fluid143Finite Volume Solution of 2D and 3D Euler and Navier-Stokes Equations173On a Conjecture Concerning the Stokes Problem in Nonsmooth Domains195On Well-Posedness of the Navier-Stokes Equations207Anisotropic and Geometric Criteria for Interior Regularity of Weak Solutions to the 3D Navier-Stokes Equations237Appendix267List of Authors269
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