Exponential Convergence to Equilibrium for Solutions of the Homogeneous Boltzmann Equation for Maxwellian Molecules

Abstract

This paper is concerned with the spatially homogeneous Boltzmann equation, with the assumption of Maxwellian interaction. We consider initial data that belong to a small neighborhood of the equilibrium, which is a Maxwellian distribution. We prove that the solution remains in another small neighborhood with the same center and converges to this equilibrium exponentially fast, with an explicit quantification.

Keywords

• Boltzmann equation
• linearized Boltzmann collision operator
• Maxwellian molecules
• Maxwellian density function
• neighborhood of equilibrium
• spatially homogeneous models