Entropic convergence for solutions of the Boltzmann equation with general physical initial data

Abstract

We show, for a particular collision kernel, that the entropy tends to its equilibrium limit for all solutions of the spatially homogeneous Boltzmann equation with finite energy, finite entropy initial data. This verses the natural conjecture following from the Boltzmann H-theorem. All previous results in this direction placed additional restrictions on the initial data beyond the physical ones considered here.