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Breakdown of smoothness for the Muskat problem

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The Muskat problem is concerned with the motion of two incompressible fluids with different densities in a porous medium. It is considered that the fluids satisfy Darcy’s law and the mass conservation equation. In this situation, the dynamics can be reduced to an equation for the interface between the fluids. In this talk we shall study the existence of singularities for it.

This talk is part of the Geometric Analysis & Partial Differential Equations seminar series.

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