On the parabolic and hyperbolic Liouville equations

2019/08/11 by Tadahiro Oh, Oh, Tadahiro, Tristan Robert +3 · 3 citations
Economics, Econometrics and Finance · Engineering · Mathematics · #35K15 #35L71 #60H15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1908.03944

openalex publication_date 2019/08/11 · openalex created_date 2021/10/11 · openalex updated_date 2026/07/28

Abstract

We study the two-dimensional stochastic nonlinear heat equation (SNLH) and stochastic damped nonlinear wave equation (SdNLW) with an exponential nonlinearity λβe^βu , forced by an additive space-time white noise. We prove local and global well-posedness of these equations, depending on the sign of λ and the size of β² > 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.)

Cited by

• Stochastic quantization of the weighted exponential QFT
• Probabilistic well-posedness of dispersive PDEs beyond variance blowup I: Benjamin-Bona-Mahony equation
• The Liouville model in the L¹ phase: coupling and extreme values

Related

• Comparing the stochastic nonlinear wave and heat equations: a case study
• The nonlinear stochastic heat equation with rough initial data:a summary of some new results
• Remarks on non-linear noise excitability of some stochastic heat equations
• Global well-posedness of the two-dimensional stochastic viscous nonlinear wave equations
• Renormalization of the two-dimensional stochastic nonlinear wave equations