The HADES seminar on Tuesday, April 16th, will be at 3:30pm in Room 939.

Speaker: Lizhe Wan, University of Wisconsin-Madison

Abstract: In this talk I will discuss the Cauchy problem of two-dimensional gravity water waves with constant vorticity. The water waves system is a nonlinear dispersive system that characterizes the evolution of free boundary fluid flows. I will describe the balanced energy estimates by Ai-Ifrim-Tataru and show that using this method, the water waves system is locally well-posed in $H^{\frac{3}{4}}\times H^{\frac{5}{4}}$. This is a low regularity well-posedness result that effectively lowers $\frac{1}{4}$ Sobolev regularity compared to the previous result.