Global well-posedness of the two-dimensional stochastic viscous nonlinear wave equations

2022/03/29 by Ruoyuan Liu, Liu, Ruoyuan
Economics, Econometrics and Finance · Engineering · Mathematics · #35L05 #35L71 #35R60 #60H15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2203.15393

openalex publication_date 2022/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study well-posedness of viscous nonlinear wave equations (vNLW) on the two-dimensional torus with a stochastic forcing. In particular, we prove pathwise global well-posedness of the stochastic defocusing vNLW with an additive stochastic forcing D^αξ, where α< \frac 12 and ξ denotes the space-time white noise.

Related

• On the two-dimensional singular stochastic viscous nonlinear wave equations
• A stochastically perturbed fluid-structure interaction problem modeled by a stochastic viscous wave equation
• Renormalization of the two-dimensional stochastic nonlinear wave equations
• Probabilistic global well-posedness for a viscous nonlinear wave equation modeling fluid-structure interaction
• On the parabolic and hyperbolic Liouville equations