The Muskat problem with surface tension and equal viscosities in subcritical $L_p$-Sobolev spaces
| Autor: | Matioc, Anca-Voichita, Matioc, Bogdan-Vasile |
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| Rok vydání: | 2020 |
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| Zdroj: | J. Elliptic Parabol. Equ., 7:635-670, 2021 |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 29 pages |
| Databáze: | arXiv |
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