Space-time paraproducts for paracontrolled calculus, 3d-PAM and multiplicative Burgers equations
Analysis of PDEs
2017-04-26 v3 Classical Analysis and ODEs
Functional Analysis
Probability
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 -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 H\"older spaces, with good continuity, that happens to be pivotal and provides one of the building blocks of higher order paracontrolled calculus.
Keywords
Cite
@article{arxiv.1506.08773,
title = {Space-time paraproducts for paracontrolled calculus, 3d-PAM and multiplicative Burgers equations},
author = {I. Bailleul and F. Bernicot and D. Frey},
journal= {arXiv preprint arXiv:1506.08773},
year = {2017}
}
Comments
v3, 56 pages. Different points about renormalisation matters have been clarified. Typos corrected