On the Boltzmann equation with soft potentials: Existence, uniqueness and smoothing effect of mild solutions

Abstract

We consider the spatially inhomogeneous Boltzmann equation without angular cutoff for soft potentials. For any given initial datum such that the mass, energy and entropy densities are bounded and the mass is away from vacuum, we establish the local-in-time existence and uniqueness of mild solutions, and further provide the first result on sharp smoothing effect in analytic space or Gevrey space for soft potentials.