Global Well-posedness of the Relativistic Boltzmann Equation

Abstract

In this paper, we prove the global existence and uniqueness of mild solution to the relativistic Boltzmann equation both in the whole space and in torus for a class of initial data with bounded velocity-weighted $L^{\infty }$-norm and some smallness on $L_x^1{L}_p^{\infty }$-norm as well as on defect mass, energy and entropy. Moreover, the asymptotic stability of the solutions is also investigated in the case of torus.

42 pages, Final version

References in corpus (3)

• Global Classical Solutions of the Boltzmann Equation without Angular Cut-off
• Asymptotic Stability of the Boltzmann Equation with Maxwell Boundary Conditions
• Global Classical Solutions to the Relativistic Boltzmann Equation without Angular Cut-off

Cited by in corpus (2)

• The hard potential relativistic Boltzmann equation in the whole space
• Local solutions for the Boltzmann equation