Boltzmann Equation with a Large Potential in a Periodic Box

Abstract

The stability of the Maxwellian of the Boltzmann equation with a large amplitude external potential $\Phi$ has been an important open problem. In this paper, we resolve this problem with a large $C3-$potential in a periodic box ${\mathbb{T}}^d$, $d\ge 3$. We use [1] in $L^p-L^{\infty }$ framework to establish the well-posedness and the $L^{\infty }-$stability of the Maxwellian ${\mu }_E(x,v)=\exp \{-\frac{|v{|}^2}{2}-\Phi (x)\}$.

References in corpus (1)

• Formation and Propagation of Discontinuity for Boltzmann Equation in Non-Convex Domains

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