On thermally driven fluid flows arising in astrophysics

We investigate a potential model for an unbounded celestial bodies of finite mass composed of a solid core and a gaseous atmosphere. The system is governed by the Navier–Stokes–Fourier–Poisson equations, incorporating no-slip boundary conditions for velocity and a specified temperature distribution on the surface of the solid core. Additionally, a positive far-field condition is imposed on the temperature. This manuscript extends the mathematical theory of open fluid systems to unbounded exterior domains addressing these physically motivated yet highly challenging combination of boundary conditions. Notably, we establish the existence of global-in-time weak solutions and demonstrate the weak–strong uniqueness principle