Quasi-linear SPDEs via a rough path approach
- Felix Otto
Abstract
Culminating in Hairer's regularity structures, there has been much recent progress in developing a robust solution theory for nonlinear stochastic partial differential equations (SPDEs). This progress is inspired by Lyons' treatment of stochastic ordinary differential equations, which is much more deterministic than Ito's approach. The main deterministic ingredient can be seen as an extended Schauder theory, so a maximal regularity theory for constant-coefficient parabolic equations in Hölder spaces, where polynomials are supplemented by more general, "rough" functions. The sole stochastic ingredient is to give an "off-line" sense to a finite number of singular products of rough functions and their distributional derivatives.
So far, this approach has been limited to SPDEs where the leading-order part is the constant-coefficient diffusion operator. In this course, we will present a treatment of the quasi-linear SPDE
Next to treating a wider class of non-linear equations, the merit is that we introduce some simpler tools. More specifically, we treat the singular product
This is joint work with Hendrik Weber.
Thursday 09:15 - 11:00
Keywords
nonlinear SPDEs, Schauder theory
Audience
MSc students, PhD students, Postdocs
Language
English