Weak solutions to the heat conducting compressible self-gravitating flows in time-dependent domains

TL;DR

This paper proves the existence of global weak solutions for heat-conducting, self-gravitating compressible fluids in moving domains, modeling viscous gaseous stars, using penalization and energy methods.

Contribution

It introduces a novel approach combining penalization and ballistic energy to handle complex boundary conditions in self-gravitating fluid flows.

Findings

Established global-in-time weak solutions

Handled non-homogeneous boundary heat flux

Extended analysis to time-dependent domains

Abstract

In this paper, we consider the heat-conducting compressible self-gravitating fluids in time-dependent domains, which typically describe the motion of viscous gaseous stars. The flow is governed by the 3-D Navier-Stokes-Fourier-Poisson equations where the velocity is supposed to fulfil the full-slip boundary condition and the temperature on the boundary is given by a non-homogeneous Dirichlet condition. We establish the global-in-time weak solution to the system. Our approach is based on the penalization of the boundary behavior, viscosity, and the pressure in the weak formulation. Moreover, to accommodate the non-homogeneous boundary heat flux, the concept of {\em ballistic energy} is utilized in this work.