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arXiv · 2307.09348

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

Kuntal Bhandari·Bingkang Huang·Šárka Nečasová
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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.

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Kuntal Bhandari, Bingkang Huang, Šárka Nečasová. 2023-07-18. Weak solutions to the heat conducting compressible self-gravitating flows in time-dependent domains. https://arxiv.org/abs/2307.09348

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