Project A1: Nonlinear interactions of rough waves

Summary:

This project is devoted to the mathematical analysis of nonlinear dispersive partial differential equations (PDEs). A key feature of a solution to a linear dispersive PDE is that it spreads out and decays, while keeping a constant L^2 norm for all times. More specifically, we will study the long-time behavior of non-linear systems involving Dirac, Wave, and Schrödinger equations in a setting where dispersive and nonlinear effects are of the same strength. Furthermore, the long-time behavior of solutions to stochastic nonlinear dispersive PDEs will be analyzed. In a parallel line of research, new estimates related to the Fourier restriction theory in harmonic analysis will be derived.

Recent Preprints: