Global existence for the Boltzmann equation in $L_v^r{L}_t^{\infty }{L}_x^{\infty }$ spaces

Abstract

We study the Boltzmann equation near a global Maxwellian. We prove the global existence of a unique mild solution with initial data which belong to the $L_v^r{L}_t^{\infty }{L}_x^{\infty }$ spaces where $r\in (1,\infty ]$ by using the excess conservation laws and entropy inequality introduced in [5].

16 pages