Analysis Seminar

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On Fundamental Solutions for Fractional Diffusion Equations with Divergence Free Drift

Speaker: Hideyuki Miura

Location: Warren Weaver Hall 1302

Date: Thursday, February 2, 2012, 11 a.m.

Synopsis:

We are concerned with fractional diffusion equations in the presence of a divergence free drift term. By using the Nash approach, we show the existence of fundamental solutions, together with the continuity estimates, under weak regularity assumptions on the drift. Our results give the alternative proof of Caffarelli-Vasseur's theorem on the regularity for the critical 2D dissipative quasi-geostrophic equations. This is a joint work with Yasunori Maekawa.