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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Jiahong Wu
Oklahoma State
Title: Models generalizing the 2D Euler and the surface quasi-geostrophic equations

Abstract: Any classical solution of the 2D incompressible Euler equation is global in time. However, it remains an outstanding open problem whether classical solutions of the surface quasi-geostrophic (SQG) equation preserve their regularity for all time. This talk presents global regularity results for a family of 2D active scalar equations in which the velocity field $u$ is determined by the scalar $theta$ through the relations
u =nabla^perp psi, quad Delta psi = P(Lambda) theta, quad Lambda=(-Delta)^{1/2}.
The 2D Euler vorticity equation corresponds to the special case $P(Lambda)=I$ while the SQG equation to the case $P(Lambda) =Lambda$. We establish the global regularity for the Loglog-Euler equation for which $P(Lambda)= (log(I+log(I-Delta)))^gamma$ with $0le gammale 1$. When a fractional dissipation term is added to the active scalar equation, the global regularity can be established for more general operators $P$. This is a joint work with Dongho Chae and Peter Constantin.

Date: Tuesday, September 28, 2010
Time: 1:30 pm
Location: Wean Hall 8220
Submitted by:  Gautam Iyer