The specular reflective boundary problem for the Boltzmann equation with soft potentials
Abstract
In this paper, we consider the specular reflective boundary problem for the onedimensional Boltzmann equation with soft potentials. It is shown that the solution converges to a global Maxwellian M+ under certain initial conditions. In order to prove this, we construct a local Maxwellian M¯ which is very close to M+ as an ansatz of M and obtain the stability of M¯ . Our proof is based on elementary energy estimates and detailed properties of Burnett functions.