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Full Description
The book is devoted to the questions of the long-time behavior of solutions for evolution equations, connected with kinetic models in statistical physics. There is a wide variety of problems where such models are used to obtain reasonable physical as well as numerical results (Fluid Mechanics, Gas Dynamics, Plasma Physics, Nuclear Physics, Turbulence Theory etc.). The classical examples provide the nonlinear Boltzmann equation. Investigation of the long-time behavior of the solutions for the Boltzmann equation gives an approach to the nonlinear fluid dynamic equations. From the viewpoint of dynamical systems, the fluid dynamic equations arise in the theory as a tool to describe an attractor of the kinetic equation.
Contents
Boundary-value problems for the Boltzmann equation in a bounded domain; existence and uniqueness theorems regarding steady solutions; steady solutions for a flow past an obstacle; Stokes paradox in the kinetic theory; the Kramers and Milne problems; external boundary problems; entropy fluxes and asymptotics in a trace of an obstacle; kinetic layer problems; initial boundary value problems for the nonlinear kinetic equations; global solutions; fluid dynamic limit of kinetic equations; convergence proofs; attractors for the Boltzmann equation; attractors for the Navier-Stokes equations; statistical solutions of the Euler equations in hydrodynamics.
