Heat semigroup and singular PDEs

Stochastic Analysis Seminar Series

I will explain a semigroup approach to the study of singular PDEs, in the line of the paracontrolled approach developed recently by Gubinelli, Imkeller and Perkowski. Starting from a heat semigroup, one can develop a functional calculus and introduce a paraproduct based on the semigroup, for which commutator estimates and Schauder estimates can be proved, together with their paracontrolled extensions. This machinery allows us to investigate singular PDEs in potentially unbounded Riemannian manifolds under mild geometric conditions. As an illustration, we study the generalized parabolic Anderson model equation and prove, under mild geometric conditions, its well-posed character, in small time on a potentially unbounded 2-dimensional Riemannian manifold, for all times for the linear parabolic Anderson model equation  in 2-dimensional unbounded manifolds. 


Ismael Balleul (Rennes 1 France)

Monday, June 8, 2015 - 14:15
to 15:15