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Frontiers in Mathematics Lecture Series

Date: September 14, 2017

Time: 4:00PM - 5:00PM

Location: Blocker 117

Speaker: Diego Cordoba, Consejo Superior de Investigaciones Científicas, Madrid, Spain


Title: Colloquium: Shift of stability and mixing solutions for the Muskat problem

Abstract: The Muskat equation governs the motion of an interface separation of two incompressible fluids in a porous media. In this talk I will present the following recent results: (1) The existence of solutions which shift stability regimes in the following sense: they start stable, then become unstable, and finally return back to the stable regime before it breaks down (joint work with J. Gomez-Serrano and A. Zlatos). (2) The existence of mixing solutions of the incompressible porous media equation for all Muskat type H^5 initial data in the fully unstable regime (joint work with A. Castro and D. Faraco).