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On the Cauchy Problem for an Approximate SQG Sharp Front Equation

Student-Run Applied & Math Seminar

Speaker: Jingyang Shu, UC Davis
Location: 2112 MSB
Start time: Wed, May 10 2017, 12:10PM

The surface quasi-geostrophic (SQG) equation describes the dynamics of atmospheric temperature and has been extensively studied in recent two decades. One interest of the 2-D SQG equation lies in its strong similarities with the 3-D incompressible Euler equations. Evolution of sharp fronts for the SQG equation is an analogue to the vortex patch problem for the 2-D Euler equations, where the temperature discontinuity is the analogue to the vorticity discontinuity. In this talk, I will discuss my joint work with Professor John Hunter concerning an approximate SQG sharp front equation. Despite a logarithmic derivative loss, we are able to prove a local well-posedness result for the Cauchy problem using a modification of Gevrey-type existence argument and obtain time-dependent-regularity Sobolev space existence.

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