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Presented By: Department of Mathematics

Differential Equations Seminar

Boussinesq and Navier-Stokes patch-type solutions: Global regularity

The main goal of this talk is to show global regularity results for parabolic fluid interface problems, without assuming any smallness on the initial data. In particular, we will consider two models: the Boussinesq system, used as an approximation in heat-induced flows, and the density-dependent Navier-Stokes.

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 Hoelder patches with C^{1+\gamma}, W^{2,\infty} and C^{2+\gamma} interfaces.

Then, we will show analogous results in relation to 96 Lions' open problem on inhomogeneous 2D Navier-Stokes density patches. We will highlight the added difficulties as well as some open questions. Speaker(s): Eduardo Garcia Juarez (University of Pennsylvania)

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