Space-time paraproducts for paracontrolled calculus, 3d-PAM and multiplicative Burgers equations

Ismaël Bailleul (1) , Frédéric Bernicot (2) , Dorothée Frey (3, 4)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LMJL - Laboratoire de Mathématiques Jean Leray
3 LMO - Laboratoire de Mathématiques d'Orsay
4 DIAM - Delft Institute of Applied Mathematics

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. Aiming that, we introduce a pair of intertwined space-time para-products on parabolic Hölder spaces, with good continuity. This constitutes to a first step in building a higher order paracontrolled calculus via semigroup methods.

Domaines: Equations aux dérivées partielles [math.AP]

Ismaël Bailleul, Frédéric Bernicot, Dorothée Frey. Space-time paraproducts for paracontrolled calculus, 3d-PAM and multiplicative Burgers equations. Annales Scientifiques de l'École Normale Supérieure, 2018, 51 (6), pp.399-1456. ⟨10.24033/asens.2378⟩. ⟨hal-02047586⟩