English

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 33-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