Speaker: Petri Laarne
Title: Almost sure solution of nonlinear wave equation: from donut to plane
Abstract:
Almost sure solution of nonlinear wave equation: from donut to plane
 
I discuss the recent preprint [arXiv:2211.16111] of Nikolay Barashkov and I, where we show almost sure well-posedness of a deterministic nonlinear wave equation on the plane. Here “almost sure” is in respect to the \phi^4 quantum field theory. In the first half of the talk, I introduce Bourgain’s invariant measure argument and construct the periodic 2D solution originally due to Oh and Thomann. In the second half I outline our main contribution: extension of these solutions to infinite volume. I also mention a weaker result for nonlinear Schrödinger equation.