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On regularity for the Muskat problem

PDE and Applied Math Seminar

Speaker: Huy Nguyen, Brown
Location: 2112 MSB
Start time: Thu, Nov 7 2019, 4:30PM

The Muskat problem models the evolution of two immiscible
fluids of varying density in a porous medium. The free interface
between the two fluids obeys a quasilinear parabolic equation, which
to leading order has a natural scaling. We will discuss our recent
results on local and global well-posedness respectively in all
subcritical spaces and certain critical spaces, allowing for
curvature singularities of the initial interface. We employ a
paradifferential calculus approach which is robust enough to
incorporate various features in the problem such as varying viscosity
and physical boundaries. We also obtain results on the vanishing
surface tension limit and the infinite depth limit.