Decay of the Boltzmann equation in spatial critical Besov space

Abstract

In this paper, we are concerned with the global existence and time decay rates of the solutions to Boltzmann equation for hard potential in the critical Chemin-Lerner type space. The evolution of the energy in negative Besov space is derived to be preserved. Our results are based on the modified trilinear estimates and some new observations. We use the Lyapunov-type inequality of the energy functionals to show the time decay rates without linear decay analysis. Compared with the previous work, the decay rates of the global solution are established for lower-regularity initial data.