Author Archives: oavadanei

Two dimensional gravity water waves with constant vorticity at low regularity

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.

Modified scattering for the three dimensional Maxwell-Dirac system

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.

Strichartz estimates for Schroedinger evolutions

The HADES seminar on Tuesday, November 7th, will be at 3:30pm in Room 740.

Speaker: Daniel Tataru

Abstract: I will provide a broad introduction to the topic of dispersive and Strichartz estimates for Schroedinger evolutions on curved backgrounds, with the final goal of describing the new Strichartz estimates proved jointly with Mihaela Ifrim in the context of 1D quasilinear Schroedinger flows.