Hydrodynamic limits of the Boltzmann equation
The problems of hydrodynamic limits for the Boltzmann equation are discussing in the six chapters book. General results are based on the Boltzmann equation and are considering the transition from kinetic theory to hydrodynamic equations. The first three chapters of the book are reviewing fundamental mathematical problems of the nonlinear Boltzmann equation solution (the Cauchy problem for the Boltzmann equation and evolution of particle distribution function of rarefied gases) and derivations of the hydrodynamic equations. Main basic problems of incompressible Navier-Stokes equations and thre solutions including the boundaries value problems are discussing. The last two chapters are devoted to the incompressible and compressible Euler equations and may be more interesting for scientists that are working on applications of rarefied bas flow to simple systems. This book may be useful for advanced graduate students and for scientists who are interesting on mathematical problems of the statistical mechanics and rarefied gases.
scientific article; zbMATH DE number 5500959