1. On the Parabolic and Hyperbolic Liouville Equations
- Author
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Tristan Robert, Tadahiro Oh, Yuzhao Wang, University of Edinburgh, Analyse, Géométrie et Modélisation (AGM - UMR 8088), Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY), Department of Mathematics and Physics, North China Electric Power University, and CY Cergy Paris Université (CY)-Centre National de la Recherche Scientifique (CNRS) more...
- Subjects
Pure mathematics ,Gaussian ,FOS: Physical sciences ,stochastic nonlinear heat equation ,Context (language use) ,Lambda ,System of linear equations ,01 natural sciences ,symbols.namesake ,Mathematics - Analysis of PDEs ,0103 physical sciences ,FOS: Mathematics ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,0101 mathematics ,35L71, 35K15, 60H15 ,Mathematical Physics ,Physics ,exponential nonlinearity ,Probability (math.PR) ,010102 general mathematics ,Multiplicative function ,Statistical and Nonlinear Physics ,Mathematical Physics (math-ph) ,White noise ,Gibbs measure ,Lipschitz continuity ,[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,Nonlinear system ,stochastic nonlinear wave equation ,Liouville equation ,symbols ,010307 mathematical physics ,Mathematics - Probability ,Analysis of PDEs (math.AP) - Abstract
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.), Comment: 70 pages. To appear in Comm. Math. Phys. Minor typos corrected more...
- Published
- 2021
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