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

0584769 - MÚ 2025 RIV SG eng J - Journal Article
Bhandari, Kuntal - Huang, B. - Nečasová, Šárka
Weak solutions to the heat conducting compressible self-gravitating flows in time-dependent domains.
Mathematical Models and Methods in Applied Sciences. Roč. 34, č. 4 (2024), s. 659-704. ISSN 0218-2025. E-ISSN 1793-6314
R&D Projects: GA ČR(CZ) GC22-08633J
Grant - others:AV ČR(CZ) AP2101
Program: Akademická prémie - Praemium Academiae
Institutional support: RVO:67985840
Keywords : compressible fluids * Navier-Stokes-Fourier-Poisson system * non-homogeneous boundary
OECD category: Pure mathematics
Impact factor: 3.5, year: 2022
Method of publishing: Limited access
https://doi.org/10.1142/S0218202524500118

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.
Permanent Link: https://hdl.handle.net/11104/0352618