Doss-Sussman transform for stochastic PDE

Date: Thursday 26th June 2025

Abstract

The well-posedness of quasilinear stochastic PDEs is often established via a stochastic analogue of the compactness argument, followed by an estimate based on the regularity of the solution. For the existence of solutions, we present a different method using the Doss-Sussmann transform. This method is well-studied, and can be applied when the noise has a specific structure, transforming the SPDE into a PDE with random coefficients. In this talk, we first review some background on stochastic PDEs, then outline the transformation method with a brief discussion of stochastic flows, and finally apply it to a 2D stochastic Landau-Lifshitz equation. This talk is based on joint work with Ben Goldys (USYD) and Christof Melcher (RWTH Aachen University).