Nonlinear Partial Differential Equations

Date: November 30, 2021

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Vedran Sohinger, University of Warwick

Title: Gibbs measures as unique KMS equilibrium states of nonlinear Hamiltonian PDEs

Abstract: Gibbs measures for nonlinear dispersive PDEs have been used as a fundamental tool in the study of low-regularity almost sure well-posedness of the associated Cauchy problem following the pioneering work of Bourgain in the 1990s. In this talk, we will discuss the connection of Gibbs measures with the Kubo-Martin-Schwinger (KMS) condition. The latter is a property characterizing equilibrium measures of the Liouville equation. In particular, we show that Gibbs measures are the unique KMS equilibrium states for a wide class of nonlinear Hamiltonian PDEs. Our proof is based on Malliavin calculus and Gross-Sobolev spaces. This is joint work with Zied Ammari.