The Boltzmann equation with specular boundary condition in convex domains

TL;DR

This paper proves the global well-posedness and stability of the Boltzmann equation with specular boundary conditions in convex domains, solving a long-standing open problem since 1977.

Contribution

It establishes the first comprehensive proof of global existence and stability for the Boltzmann equation with specular reflection in convex domains.

Findings

Global well-posedness and stability proven

Solution applies to initial data near Maxwellian

Addresses open problem from 1977

Abstract

We establish the global-wellposedness and stability of the Boltzmann equation with the specular reflection boundary condition in general smooth convex domains when an initial datum is close to the Maxwellian with or without a small external potential. In particular, we have completely solved the long standing open problem after an announcement of [20] in 1977.