Paracontrolled calculus for quasilinear singular PDEs

Ismaël Bailleul (1, 2) , Antoine Mouzard (1, 2)

1 UR - Université de Rennes
2 IRMAR - Institut de Recherche Mathématique de Rennes

We develop further in this work the high order paracontrolled calculus setting to deal with the analytic part of the study of quasilinear singular PDEs. A number of continuity results for some operators are proved for that purpose. Unlike the regularity structures approach of the subject by Gerencser & Hairer and Otto, Sauer, Smith & Weber, or Furlan and Gubinelli' study of the two dimensional quasilinear parabolic Anderson model equation, we do not use parametrised families of models or paraproducts to set the scene. We use instead infinite dimensional paracontrolled structures that we introduce here.

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Ismaël Bailleul, Antoine Mouzard. Paracontrolled calculus for quasilinear singular PDEs. Stochastics and Partial Differential Equations: Analysis and Computations, 2022, ⟨10.1007/s40072-022-00239-9⟩. ⟨hal-02428604⟩