L p solutions to the Cauchy problem of the BGK equation

Abstract

The BGK model of the Boltzmann equation plays an important role in the kinetic theory of rarefied gases. Some existence and uniqueness results of solutions to its Cauchy problem were established for large initial data under various circumstances [see, for example, Perthame, B., “Global existence to the BGK model of Boltzmann equation,” J. Differ. Equations 82, 191–205 (1989)]. In this paper, by establishing some weighted Lp estimates of the hydrodynamical quantities of a gas, we prove the existence theorem of the Lp solutions to the Cauchy problem and establish the propagation properties of the Lp moments for this kind of solutions.