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# M. E. Taylor Analysis and PDE Seminar – Lizhe Wan (UW-Madison)

## April 10 @ 3:30 pm - 4:30 pm

**Gravity water waves with constant vorticity at low regularity and balanced energy estimates**

**Abstract**. In this talk I will talk about 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 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.