Variational rotating solutions to non-isentropic Euler-Poisson equations with prescribed total mass

TL;DR

This paper establishes the existence of variational rotating solutions for the non-isentropic Euler-Poisson equations with a fixed total mass, extending previous isentropic and non-isentropic results through a new variational approach.

Contribution

It introduces a novel variational structure for the non-isentropic Euler-Poisson equations that enforces a prescribed total mass, extending prior work to a more general setting.

Findings

Existence of variational rotating solutions proven

Extension from isentropic to non-isentropic cases

New variational framework for fixed total mass

Abstract

This paper proves the existence of variational rotating solutions to the compressible non-isentropic Euler-Poisson equations with prescribed total mass. This extends the result of the isentropic case [Auchmuty and Beals, Arch. Ration. Mech. Anal., 1971] to the non-isentropic case. Compared with the previous result of variational rotating solutions in non-isentropic case [Wu, Journal of Differential Equations, 2015], to keep the constraint of a prescribed finite total mass, the author establishes a new variational structure the non-isentropic Euler-Poisson equations.