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 3D Navier–Stokes–Fourier–Poisson equations where the velocity is supposed to fulfill 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 ballistic energy is utilized in this work.

在本文中，我们考虑时间相关域中的导热可压缩自重力流体，它通常描述粘性气态恒星的运动。流动由 3D Navier-Stokes-Fourier-Poisson 方程控制，其中速度应满足全滑移边界条件，边界上的温度由非齐次狄利克雷条件给出。我们建立了系统的全局及时弱解。我们的方法基于弱公式中边界行为、粘度和压力的惩罚。此外，为了适应非均匀边界热通量，本工作中利用了弹道能的概念。