## Differential and Integral Equations

### Uniqueness for the BGK-equation in $\mathbb{R}^N$ and rate of convergence for a semi-discrete scheme

Stéphane Mischler

#### Abstract

We prove estimates, in weighted $L^\infty$ spaces, for solutions of the BGK equation in the whole space and lower bound on the associated macroscopic density. $L^\infty$ bound on the macroscopic object $\rho, u$ and $T$ are deduced. Then we may show uniqueness of the solution of the BGK equation with $L^\infty$-bound assumption on the initial data, propagation of estimates on derivatives. As an application, with a BV-bound assumption on the initial data we get the convergence with rate $(\Delta t)^{1/2}$ of a time semi-discretized scheme to the solution.

#### Article information

Source
Differential Integral Equations, Volume 9, Number 5 (1996), 1119-1138.

Dates
First available in Project Euclid: 6 May 2013

Mischler, Stéphane. Uniqueness for the BGK-equation in $\mathbb{R}^N$ and rate of convergence for a semi-discrete scheme. Differential Integral Equations 9 (1996), no. 5, 1119--1138. https://projecteuclid.org/euclid.die/1367871533