Existence and Uniqueness Theorems for the Boltzmann Equation

Abstract

In general, the situation which arises when mathematically studying the Boltzmann equation may be outlined as follows. There are two well-studied limiting regimes. The first of them is the so-called free-particle flow, where the particles do not interact. The second one corresponds to thermodynamic equilibrium which is described by the Maxwell distribution. Almost all theorems which are known at present guarantee existence of a solution of boundary problems in situations which are close to one of the mentioned regimes. The only problem for which one succeeds to prove global eixtence without serious restrictions on initial deta, is the Cauchy problem for a homogeneous gas.