The Muskat problem in subcritical Lp-Sobolev spaces

Bogdan-Vasile Matioc (University of Regensburg)

09-Jul-2020, 14:00-14:50 (4 years ago)

Abstract: The Muskat problem is a classical mathematical model which describes the motion of two immiscible and incompressible Newtonian fluids in an homogeneous porous medium. The mathematical model posed in the entire plane can be formulated as an evolution equation for the function that parametrizes the free boundary between the fluids. When neglecting surface tension effects, the evolution equation is fully nonlinear and nonlocal and it involves singular integral operators defined by kernels that depend nonlinearly on the unknown. We prove that the evolution problem is of parabolic type in the regime where the Rayleigh-Taylor condition is satisfied. Based upon this feature we establish the well posedness of the Muskat problem in all subcritical Lp-Sobolev spaces together with a parabolic smoothing property. This is a joint work with Helmut Abels.

analysis of PDEs

Audience: researchers in the topic


PDE seminar via Zoom

Organizer: Quoc-Hung Nguyen*
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