Birkhauser Verlag, 2004. — 162 p. — (Advances in Mathematical Fluid Mechanics). — ISBN 3-7643-7104-8.This volume consists of five research articles, each dedicated to a significant topic in the mathematical theory of the Navier-Stokes equations, for compressible and incompressible fluids, and to related questions. All results given here are new and represent a noticeable contribution to the subject. One of the most famous predictions of the Kolmogorov theory of turbulence is the so-called Kolmogorov-obukhov five-thirds law. As is known, this law is heuristic and, to date, there is no rigorous justification. The article of A. Biryuk deals with the Cauchy problem for a multi-dimensional Burgers equation with periodic boundary conditions. Contents On Multidimensional Burgers Type Equations with Small Viscosity On the Global Well-posedness and Stability of the Navier-Stokes and the Related Equations The Commutation Error of the Space Averaged Navier-Stokes Equations on a Bounded Domain The Nonstationary Stokes and Navier-Stokes Flows Through an Aperture Asymptotic Behavior at Infinity of Exterior Three-dimensional Steady Compressible Flow
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