Analysis Seminar

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Paracontrolled Calculus and Singular PDEs Through the Heat Semigroup

Speaker: Frederic Bernicot, University of Nantes

Location: Warren Weaver Hall 1302

Date: Thursday, November 17, 2016, 11 a.m.

Synopsis:

We will present the main idea of the paracontrolled calculus, which was recently introduced in the Euclidean situation by Gubinelli, Imkeller and Perkowski. This gives an alternative approach to Hairer's theory in order to deal with singular (stochastic) PDEs, such as the Parabolic Anderson Model (2D-3D) and Burgers equations. Indeed, it relies on the following fact: the paraproduct (as a singular bilinear operator) is the well-suited analytic tool, in order to isolate the stochastic cancellations in nonlinearities. We will then explain how we can extend it in many various situations, given by a heat semigroup with gradient estimates.