Moisture dynamics with phase changes coupled to heat-conducting, compressible fluids
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911510751608832 |
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| author | Brandt, Felix Hieber, Matthias Ma, Lin Zöchling, Tarek |
| author_facet | Brandt, Felix Hieber, Matthias Ma, Lin Zöchling, Tarek |
| contents | It is shown that a model coupling the heat-conducting compressible Navier-Stokes equations to a micro-physics model of moisture in air is locally strongly well-posed for large data in suitable function spaces and strongly well-posed on $[0,τ]$ for every $τ> 0$ for small initial data. This seems to be the first result on $[0,τ]$ for arbitrary $τ> 0$ for a model coupling moisture dynamics to heat-conducting, compressible Navier-Stokes equations. A key feature of the micro-physics model is that it also includes phase changes of water in moist air. These phase changes are associated with large amounts of latent heat and thus result in a strong coupling to the thermodynamic equation. The well-posedness results are obtained by means of a Lagrangian approach, which allows to treat the hyperbolicity in the continuity equation. More precisely, optimal $\mathrm{L}^p$-$\mathrm{L}^q$ estimates are shown for the linearized system, leading to the local well-posedness result by a fixed point argument and suitable nonlinear estimates. For the well-posedness result on $[0,τ]$ for arbitrary $τ> 0$, a refined analysis of the linearized problem close to equilibria is carried out, and the roughness of the source term, induced by the phase changes, requires to establish delicate a priori bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14931 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moisture dynamics with phase changes coupled to heat-conducting, compressible fluids Brandt, Felix Hieber, Matthias Ma, Lin Zöchling, Tarek Analysis of PDEs 35K59, 35Q35, 35Q86, 76N10 It is shown that a model coupling the heat-conducting compressible Navier-Stokes equations to a micro-physics model of moisture in air is locally strongly well-posed for large data in suitable function spaces and strongly well-posed on $[0,τ]$ for every $τ> 0$ for small initial data. This seems to be the first result on $[0,τ]$ for arbitrary $τ> 0$ for a model coupling moisture dynamics to heat-conducting, compressible Navier-Stokes equations. A key feature of the micro-physics model is that it also includes phase changes of water in moist air. These phase changes are associated with large amounts of latent heat and thus result in a strong coupling to the thermodynamic equation. The well-posedness results are obtained by means of a Lagrangian approach, which allows to treat the hyperbolicity in the continuity equation. More precisely, optimal $\mathrm{L}^p$-$\mathrm{L}^q$ estimates are shown for the linearized system, leading to the local well-posedness result by a fixed point argument and suitable nonlinear estimates. For the well-posedness result on $[0,τ]$ for arbitrary $τ> 0$, a refined analysis of the linearized problem close to equilibria is carried out, and the roughness of the source term, induced by the phase changes, requires to establish delicate a priori bounds. |
| title | Moisture dynamics with phase changes coupled to heat-conducting, compressible fluids |
| topic | Analysis of PDEs 35K59, 35Q35, 35Q86, 76N10 |
| url | https://arxiv.org/abs/2512.14931 |