A survey for the Muskat problem and a new estimate
This paper shows a summary of mathematical results about the Muskat problem. The main concern is well-posed scenarios which include the possible formation of singularities in finite time or existence of solutions for all time. These questions are important in mathematical physics but also have a str...
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| Format: | article |
| Status: | Versión enviada para evaluación y publicación |
| Publication Date: | 2017 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/49241 |
| Online Access: | http://hdl.handle.net/11441/49241 https://doi.org/10.1007/s40324-016-0078-9 |
| Access Level: | Open access |
| Keyword: | Porous medium Darcy’s law Muskat problem Maximum principle |
| Summary: | This paper shows a summary of mathematical results about the Muskat problem. The main concern is well-posed scenarios which include the possible formation of singularities in finite time or existence of solutions for all time. These questions are important in mathematical physics but also have a strong mathematical interest. Stressing some recent results of the author, we also give a new estimate for the problem in the last section. Initial data with L2 decay and slope less than one provide weak solutions which satisfy a parabolic inequality as in the linear regime. |
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