Exponential Convergence to the Maxwell Distribution For Spatially Inhomogenous Boltzmann Equations

2016/03/21 by Gang, Zhou
#35Q70 #76P05 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1603.06642

Abstract

We consider the rate of convergence of solutions of spatially inhomogenous Boltzmann equations, with hard sphere potentials, to some equilibriums, called Maxwellians. Maxwellians are spatially homogenous static Maxwell velocity distributions with different temperatures and mean velocities. We study solutions in weighted space L¹(ℝ³× \mathbbT³). We prove a conjecture of C. Villani: assume the solution is sufficiently localized and sufficiently smooth, then the solution, in L¹-space, converges to a Maxwellian, exponentially fast in time.

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