Entropy solutions to macroscopic IPM
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866918173656219648 |
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| author | Castro, Ángel Faraco, Daniel Gebhard, Björn |
| author_facet | Castro, Ángel Faraco, Daniel Gebhard, Björn |
| contents | We investigate maximal potential energy dissipation as a selection criterion for subsolutions (coarse grained solutions) in the setting of the unstable Muskat problem. We show that both, imposing this criterion on the level of convex integration subsolutions, and the strategy of Otto based on a relaxation via minimizing movements, lead to the same nonlocal conservation law. Our main result shows that this equation admits an entropy solution for unstable initial data with an analytic interface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03637 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Entropy solutions to macroscopic IPM Castro, Ángel Faraco, Daniel Gebhard, Björn Analysis of PDEs We investigate maximal potential energy dissipation as a selection criterion for subsolutions (coarse grained solutions) in the setting of the unstable Muskat problem. We show that both, imposing this criterion on the level of convex integration subsolutions, and the strategy of Otto based on a relaxation via minimizing movements, lead to the same nonlocal conservation law. Our main result shows that this equation admits an entropy solution for unstable initial data with an analytic interface. |
| title | Entropy solutions to macroscopic IPM |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2309.03637 |