| Abstract: |
| The Muskat and Peskin problems model very different physical phenomena, but both are described by quasilinear and nonlocal parabolic partial differential equations. The former describes the movement of two immiscible and incompressible fluids filtrating a porous medium, while the latter corresponds to an elastic filament immersed in a Stokesian fluid. We will study the small data critical regularity theory for these two models and show that interfaces with corners desingularize in time. |
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