In this talk I will review some recent developments concerning non-uniqueness of solutions to stochastic PDEs via the technique of convex integration adapted to probabilistic settings. Examples of stochastic PDEs include Navier-Stokes equations, Euler equations, Boussinesq system, and magnetohydrodynamics system, some of which have diffusion in the form of fractional Laplacian with certain powers. The types of noise include additive nose, linear multiplicative noise, nonlinear noise, and space-time white noise (although noise have some further hypothesis). Some of these non-uniqueness results are path-wise while some are in law, and solutions are probabilistically strong.
Recent developments on non-uniqueness of stochastic PDEs via convex integration
Kazuo Yamazaki, Texas Tech University
2022 AWM Research Symposium
Deterministic and Probabilistic Approaches for Nonlinear PDEs