Global well-posedness of homogeneous Boltzmann equation in modulation spaces

Abstract

In this paper, we study the Cauchy problem of Boltzmann equation with soft potential in modulation spaces. Our aim is to obtain the global existence of solution to the space-homogeneous Boltzmann equation. To realize this goal, the boundedness of Boltzmann operator in modulation space is established. In addition, Banach fixed-point theorem is applied with careful estimate of time integral for the contraction mapping.