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

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

Conference Paper (2018)

Author(s)

Ismael Bailleul (Institut de Recherche Mathematiques de Rennes)

Frederic Bernicot (Université de Nantes)

Dorothee Frey (TU Delft - Electrical Engineering, Mathematics and Computer Science, ENS-PSL Research University & CNRS)

Research Group

Analysis

DOI related publication

https://doi.org/10.24033/asens.2378 Final published version

To reference this document use

https://resolver.tudelft.nl/uuid:ea3ff6f5-8780-40a4-b4f7-f7657f13724d

More Info

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Publication Year

2018

Language

English

Research Group

Analysis

Volume number

51

Pages (from-to)

1399-1456

Page Views

179

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.