Well-posedness and stability results for some periodic Muskat problems

27 Apr 2018 Matioc Bogdan-Vasile

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 $H^r(\mathbb{S})$ for each $r\in(2,3)$... (read more)

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