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Analysis Seminar

Thursday, October 11, 2018 - 3:00pm

Eduardo Garcia-Juarez

University of Pennsylvania


University of Pennsylvania


A fundamental question in fluid mechanics free boundary problems is to study if a free interface evolving with the fluid flow preserves in time its initial regularity. The other possible scenario involves the appearance of finite time singularities. In this talk, we will first show that 2D sharp fronts of temperature modeled by the Boussinesq equations propagate their structure and interface regularity globally in time. The results also hold in 3D and include initial temperatures given by piecewise H\"older patches with C^{1+\gamma}, W^{2,\infty} and C^{2+\gamma} interfaces. Then, using more involved techniques, we will show analogous results that solve 96 Lions' open problem on inhomogeneous 2D Navier-Stokes density patches.