Space-time paraproducts for paracontrolled calculus, 3D-pam and multiplicative burgers equations

Bailleul, Ismael; Bernicot, Frederic; Frey, Dorothee

Space-time paraproducts for paracontrolled calculus, 3D-pam and multiplicative burgers equations

Conference paper (2018)

Authors

Ismael Bailleul Institut de Recherche Mathematiques de Rennes

Frederic Bernicot Université de Nantes

Dorothee Frey Analysis, ENS-PSL Research University & CNRS

Research Group

Analysis

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Published Date

2018

Language

English

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Research Group

Analysis

Abstract

We sharpen in this work the tools of paracontrolled calculus in order to provide a complete analysis of the parabolic Anderson model equation and Burgers system with multiplicative noise, in a 3-dimensional Riemannian setting, in either bounded or unbounded domains. With that aim in mind, we introduce a pair of intertwined space-time paraproducts on parabolic Hölder spaces, with good continuity, that happens to be pivotal and provides one of the building blocks of higher order paracontrolled calculus.

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