Unconditional stability of equilibria in thermally driven compressible fluids
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909060099473408 |
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| author | Feireisl, Eduard Lu, Yong Sun, Yongzhong |
| author_facet | Feireisl, Eduard Lu, Yong Sun, Yongzhong |
| contents | We show that small perturbations of the spatially homogeneous equilibrium of a thermally driven compressible viscous fluid are globally stable. Specifically, any weak solution of the evolutionary Navier--Stokes--Fourier system driven by thermal convection converges to an equilibrium as time goes to infinity. The main difficulty to overcome is the fact the problem does not admit any obvious Lyapunov function. The result applies, in particular, to the Rayleigh--B\' enard convection problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01494 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unconditional stability of equilibria in thermally driven compressible fluids Feireisl, Eduard Lu, Yong Sun, Yongzhong Analysis of PDEs We show that small perturbations of the spatially homogeneous equilibrium of a thermally driven compressible viscous fluid are globally stable. Specifically, any weak solution of the evolutionary Navier--Stokes--Fourier system driven by thermal convection converges to an equilibrium as time goes to infinity. The main difficulty to overcome is the fact the problem does not admit any obvious Lyapunov function. The result applies, in particular, to the Rayleigh--B\' enard convection problem. |
| title | Unconditional stability of equilibria in thermally driven compressible fluids |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.01494 |