CMU Campus
Center for                           Nonlinear Analysis
CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact
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