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.

The HADES seminar on Tuesday, March 19th, will be at 3:30pm in Room 939.

Speaker: Mihaela Ifrim

Abstract: In this work we prove global well-posedness for the massive Maxwell-Dirac equation in the Lorentz gauge in $\mathbb{R}^{1+3}$, for small and localized initial data, as well as modified scattering for the solutions.  In doing so, we heuristically exploit the close connection between massive  Maxwell-Dirac and the  wave-Klein-Gordon equations, while  developing a novel approach which applies directly at the level of the Dirac equations.  This is joint work with Sebastian Herr and Martin Spitz.