Uniform stability of solutions of Boltzmann equation for soft potential with external force

The study of Cauchy problem of the Boltzmann equation is important in both theory and applications. Existence of global solutions to the equation and uniform stability of solutions in the absence of external force were introduced in the previous work on the Boltzmann equation. In this paper, we will investigate the uniform stability of solutions in L 1 for the Cauchy problem of the Boltzmann equation when there is an external force for the case of soft potentials.