Weak solutions to incompressible heat-conducting motions with large flux
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911026207784960 |
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| author | Rencławowicz, Joanna Zajączkowski, Wojciech M. |
| author_facet | Rencławowicz, Joanna Zajączkowski, Wojciech M. |
| contents | We analyze the problem for viscous incompressible heat-conduc\-ting fluid in a finite cylinder with large inflow and outflow, modelled with Navier-Stokes equations coupled with the heat equation. We prove energy estimate without restrictions on the magnitudes of the external force, initial data, inflow and outflow. In order to estimate nonlinear terms we use weighted spaces. Next, using Galerkin approximation, we show existence of weak solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22155 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak solutions to incompressible heat-conducting motions with large flux Rencławowicz, Joanna Zajączkowski, Wojciech M. Analysis of PDEs Primary 35Q30, Secondary 76D03, 76D05 We analyze the problem for viscous incompressible heat-conduc\-ting fluid in a finite cylinder with large inflow and outflow, modelled with Navier-Stokes equations coupled with the heat equation. We prove energy estimate without restrictions on the magnitudes of the external force, initial data, inflow and outflow. In order to estimate nonlinear terms we use weighted spaces. Next, using Galerkin approximation, we show existence of weak solutions. |
| title | Weak solutions to incompressible heat-conducting motions with large flux |
| topic | Analysis of PDEs Primary 35Q30, Secondary 76D03, 76D05 |
| url | https://arxiv.org/abs/2506.22155 |