The Muskat problem with critical regularity

SEMINARIO DE ECUACIONES DIFERENCIALES

Conferenciante: Eduardo García Juárez (Universidad de Sevilla)

Abstract: The Muskat problem models the movement of two immiscible and incompressible fluids in a porous medium. The problem can be reduced to an evolution equation for the free interface, that satisfies a quasilinear and nonlocal partial differential equation. We will first review the main features of the problem and describe previous results, and we will conclude with two recent results where the regularity of the interface is critical with respect to the natural scaling of the equation: a rising bubble and an interface with corners.