Weak solutions to the heat conducting compressible self-gravitating flows in time-dependent domains
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914642853363712 |
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| author | Bhandari, Kuntal Huang, Bingkang Nečasová, Šárka |
| author_facet | Bhandari, Kuntal Huang, Bingkang Nečasová, Šárka |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_09348 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Weak solutions to the heat conducting compressible self-gravitating flows in time-dependent domains Bhandari, Kuntal Huang, Bingkang Nečasová, Šárka Analysis of PDEs 35D30, 35Q35, 76N10 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. |
| title | Weak solutions to the heat conducting compressible self-gravitating flows in time-dependent domains |
| topic | Analysis of PDEs 35D30, 35Q35, 76N10 |
| url | https://arxiv.org/abs/2307.09348 |