On the parabolic and hyperbolic Liouville equations

Tadahiro Oh (1) , Tristan Robert (2) , Yuzhao Wang (3)

1 Edin. - University of Edinburgh
2 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
3 Department of Mathematics and Physics

We study the two-dimensional stochastic nonlinear heat equation (SNLH) and stochastic damped nonlinear wave equation (SdNLW) with an exponential nonlinearity $\lambda\beta e^{\beta u }$, forced by an additive space-time white noise. We prove local and global well-posedness of these equations, depending on the sign of $\lambda$ and the size of $\beta^2 > 0$, and invariance of the associated Gibbs measures. See the abstract of the paper for a more precise abstract. (Due to the limit on the number of characters for an abstract set by arXiv, the full abstract can not be displayed here.)

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

Tadahiro Oh, Tristan Robert, Yuzhao Wang. On the parabolic and hyperbolic Liouville equations. Communications in Mathematical Physics, 2021, ⟨10.1007/s00220-021-04125-8⟩. ⟨hal-02434800⟩