Local well-posedness for Euler-Poisson fluids with non-zero heat conduction

TL;DR

This paper proves local well-posedness for multidimensional Euler-Poisson equations with heat conduction, using advanced analytical techniques in critical Besov spaces to handle the complex coupling effects.

Contribution

It establishes the first local well-posedness result for these coupled systems with non-zero heat conduction in critical Besov spaces, introducing a new Moser-type inequality.

Findings

Proves local existence and uniqueness of classical solutions

Develops a new Moser-type inequality for analysis

Handles complex coupling effects in Euler-Poisson systems

Abstract

We consider the multidimensional Euler-Poisson equations with non-zero heat conduction, which consist of a coupled hyperbolic-parabolic-elliptic system of balance laws. We make a deep analysis on the coupling effects and establish a local well-posedness of classical solutions to the Cauchy problem pertaining to data in the critical Besov space. Proof mainly relies on a standard iteration argument. To achieve it, a new Moser-type inequality is developed by the Bony' decomposition.