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Recents results for SQG sharp front and the Muskat problem

PDE and Applied Math Seminar

Speaker: Francisco Gancedo, Universidad de Sevilla
Location: 2112 MSB
Start time: Tue, May 24 2016, 4:10PM

In this talk we study two scenarios in contour dynamics. The Muskat problem, where the dynamics of two fluids of different nature in porous media are modeled. And front of temperature driven by the Surface Quasi-geostrophic equation (SQG). The dynamics for both free boundary problems are not well understood. A main issue for both free boundary problems is finite time singularity formation versus global in time results. For Muskat we show a blow-up criteria for solution to became singular in a stable case. For SQG a uniqueness results for the free boundary modulo reparameterization is given.