Rigidity of acute angled corners for one phase Muskat interfaces
We consider the one-phase Muskat problem modeling the dynamics of the free boundary of a single fluid in porous media. In the stable regime, we prove local well-posedness for fluid interfaces that are general curves and can have singularities. In particular, the free boundary can have acute angle co...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/349474 |
| Acceso en línea: | http://hdl.handle.net/10261/349474 https://api.elsevier.com/content/abstract/scopus_id/85143870919 |
| Access Level: | acceso abierto |
| Palabra clave: | Muskat equation Rigidity Singularities |
| Sumario: | We consider the one-phase Muskat problem modeling the dynamics of the free boundary of a single fluid in porous media. In the stable regime, we prove local well-posedness for fluid interfaces that are general curves and can have singularities. In particular, the free boundary can have acute angle corners or cusps. Moreover, we show that isolated corners/cusps on the interface must be rigid, meaning the angle of the corner is preserved for a finite time, there is no rotation at the tip, the particle at the tip remains at the tip and the velocity of that particle at the tip points vertically downward. |
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