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Title:
Introduction to Stochastic Partial Differential Equations

Speaker:
Arnaud Debussche

Abstract:
SPDEs with white noise. I will focus on the stochastic Burgers and reaction-diffusion equations which will be first solved with spatially smooth noise and then with space time white noise. The case of the reaction-diffusion equation in dimension 2 is already not so obvious since the solutions are not expected to be function valued processes. The case of dimension 3 is much more difficult and has been solved only recently by Martin Hairer. I will not explain in details his theory on regularity structure, this would take too much time. However, I will explain why the problem is so difficult and give few hints on this difficult theory. No prerequisite on stochastic calculus is expected from the audience.

Link:
https://www.msri.org/workshops/760/schedules/20132

Workshop:
MSRI- Introductory Workshop: Randomness and long time dynamics in nonlinear evolution differential equations