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The Muskat problem with surface tension and equal viscosities in subcritical Lp-Sobolev spaces

URN to cite this document:
urn:nbn:de:bvb:355-epub-462444
DOI to cite this document:
10.5283/epub.46244
Matioc, Anca-Voichita ; Matioc, Bogdan-Vasile
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Date of publication of this fulltext: 07 Jul 2021 05:39


Abstract

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)}. ...

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