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The Muskat problem in two dimensions: equivalence of formulations, well-posedness, and regularity results

Matioc, Bogdan-Vasile



Abstract

We consider the Muskat problem describing the motion of two unbounded immiscible fluid layers with equal viscosities in vertical or horizontal two-dimensional geometries. We first prove that the mathematical model can be formulated as an evolution problem for the sharp interface separating the two fluids, which turns out to be, in a suitable functional-analytic setting, quasilinear and of ...

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