Global Existence for the Ellipsoidal BGK Model with Initial Large Oscillations

TL;DR

This paper proves the global existence of solutions to the ellipsoidal BGK model with large initial oscillations, extending understanding of kinetic models in fluid dynamics.

Contribution

It establishes the first global existence result for the ellipsoidal BGK model with large initial oscillations, inspired by recent Boltzmann equation studies.

Findings

Global existence of mild solutions is proven.

Applicable to initial data with large oscillations.

Method inspired by Boltzmann equation analysis.

Abstract

The ellipsoidal BGK model was introduced in \cite{Ho} to fit the correct Prandtl number in the Navier-Stokes approximation of the classical BGK model. In the paper we establish the global existence of mild solutions to the Cauchy problem on the model for a class of initial data allowed to have large oscillations. The proof is motivated by a recent study of the same topic on the Boltzmann equation in \cite{DHWY}.