The Muskat problem with surface tension and equal viscosities in subcritical $L_p$-Sobolev spaces
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866911851872256000 |
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| author | Matioc, Anca-Voichita Matioc, Bogdan-Vasile |
| author_facet | Matioc, Anca-Voichita Matioc, Bogdan-Vasile |
| contents | In this paper we establish the well-posedness of the Muskat problem with surface tension and equal viscosities in the subcritical Sobolev spaces $W^s_p(\mathbb{R})$, where ${p\in(1,2]}$ and ${s\in(1+1/p,2)}$. This is achieved by showing that the mathematical model can be formulated as a quasilinear parabolic evolution problem in $W^{\overline{s}-2}_p(\mathbb{R})$, where ${\overline{s}\in(1+1/p,s)}$. Moreover, we prove that the solutions become instantly smooth and we provide a criterion for the global existence of solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_12261 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Muskat problem with surface tension and equal viscosities in subcritical $L_p$-Sobolev spaces Matioc, Anca-Voichita Matioc, Bogdan-Vasile Analysis of PDEs 35R37, 76D27, 35K59 In this paper we establish the well-posedness of the Muskat problem with surface tension and equal viscosities in the subcritical Sobolev spaces $W^s_p(\mathbb{R})$, where ${p\in(1,2]}$ and ${s\in(1+1/p,2)}$. This is achieved by showing that the mathematical model can be formulated as a quasilinear parabolic evolution problem in $W^{\overline{s}-2}_p(\mathbb{R})$, where ${\overline{s}\in(1+1/p,s)}$. Moreover, we prove that the solutions become instantly smooth and we provide a criterion for the global existence of solutions. |
| title | The Muskat problem with surface tension and equal viscosities in subcritical $L_p$-Sobolev spaces |
| topic | Analysis of PDEs 35R37, 76D27, 35K59 |
| url | https://arxiv.org/abs/2010.12261 |