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Well-Posedness and Stability Results for Some Periodic Muskat Problems

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Matioc, Bogdan‑Vasile
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Date of publication of this fulltext: 08 Feb 2021 10:31


We study the two-dimensional Muskat problem in a horizontally periodic setting and for fluids with arbitrary densities and viscosities. We show that in the presence of surface tension effects the Muskat problem is a quasilinear parabolic problem which is well-posed in the Sobolev space H-r(S) for each r is an element of(2,3). When neglecting surface tension effects, the Muskat problem is a fully ...


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