Description
Title: A (brief) introduction to Gibbs measures for the nonlinear Schrödinger equation
Abstract: In this talk I will give an introduction to Gibbs measures for the nonlinear Schrödinger equation. The construction of global solutions to dispersive PDEs usually relies on the conservation of quantities like the energy and the mass. For lower regularity functions, these quantities are infinite, so cannot be used. Instead one introduces an invariant measure, which can act as a substitute for the conserved quantities.
I give the heuristic ideas for the construction the Gibbs measure, and also sketch the details of the rigorous construction. I will also discuss how to use the Gibbs measure to construct global solutions to the nonlinear Schrödinger equation.
