EVENT DETAILS AND ABSTRACT

Title: Infinite-volume Gibbs measures and dynamics for defocusing NLS
Speaker: Phil Sosoe
Speaker Info: Harvard University
Brief Description:
Special Note:
Abstract:

In the 1990s, Jean Bourgain proved well-posedness of the nonlinear Schroedinger equation on the 1D torus. He used these results to construct global solutions in the support of certain invariant measures of Gibbs type. He later extended these results to the real line, in the defocusing case, under certain restrictions on the nonlinearity. I will explain how the identification of the invariant measures as periodic versions of diffusions simplifies Bourgain's argument, and allows us to extend the range of nonlinearities for which his construction works, and construct dynamics for the NLS with Dirichlet boundary conditions on a half-line. Joint work with Tadahiro Oh and Jeremy Quastel.