Viscosity analysis on the spatially homogeneous Boltzmann equation

摘要

In this paper we study the existence and uniqueness of the solution to the viscosity equation ∂_tf = δΔf + Q(f, f) with collision kernel B(|v - v_*|,ω) = |v - v_*|~γb(cosθ) and δ > 0 small enough; especially show that the solution f can approach the one of unperturbed equation in L_k~1-norm while δ goes to 0. Our method mainly relies on the interpolation inequalities and the decomposition of Q~+.