The Verigin problem with phase transition as a Wasserstein flow
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914285320404992 |
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| author | Kubin, Anna Laux, Tim Marveggio, Alice |
| author_facet | Kubin, Anna Laux, Tim Marveggio, Alice |
| contents | We study the modeling of a compressible two-phase flow in a porous medium. The governing free boundary problem is known as the Verigin problem with phase transition. We introduce a novel variational framework to construct weak solutions. Our approach reveals the gradient-flow structure of the system by adopting a minimizing movement scheme using the Wasserstein distance. We prove the convergence of the scheme, obtaining ``relaxed" distributional solutions in the limit that satisfy an optimal energy-dissipation rate. Under the additional assumptions that $d \geq 3$ and that the discrete mass densities are uniformly Muckenhoupt weights, we show that the limit is the characteristic function of a set of finite perimeter in the region where there is no vacuum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20001 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Verigin problem with phase transition as a Wasserstein flow Kubin, Anna Laux, Tim Marveggio, Alice Analysis of PDEs 35R35, 49Q22, 35R37, 76D27, 76S05, 35A01, 35D30 We study the modeling of a compressible two-phase flow in a porous medium. The governing free boundary problem is known as the Verigin problem with phase transition. We introduce a novel variational framework to construct weak solutions. Our approach reveals the gradient-flow structure of the system by adopting a minimizing movement scheme using the Wasserstein distance. We prove the convergence of the scheme, obtaining ``relaxed" distributional solutions in the limit that satisfy an optimal energy-dissipation rate. Under the additional assumptions that $d \geq 3$ and that the discrete mass densities are uniformly Muckenhoupt weights, we show that the limit is the characteristic function of a set of finite perimeter in the region where there is no vacuum. |
| title | The Verigin problem with phase transition as a Wasserstein flow |
| topic | Analysis of PDEs 35R35, 49Q22, 35R37, 76D27, 76S05, 35A01, 35D30 |
| url | https://arxiv.org/abs/2601.20001 |