Work

Quasi-invariance of the Gaussian measure for the two-dimensional stochastic cubic nonlinear wave equation

Year: 2025

Type: article

Abstract: We consider the stochastic damped nonlinear wave equation $$\partial _t^{2}u+\partial _t u+u-\Delta u +u^{3} = \sqrt{2} {\langle {\nabla }\rangle ^{-s}} \xi $$ ∂ t 2 u + ∂ t u + u - Δ u + u 3 = 2 ⟨ ∇ ⟩ - s ξ on the two-dimensional torus $$\mathbb T^2$$ T 2 , where $$\xi $$ ξ denotes a space-time white noise and $$s>0$$ s > 0 . We show that the measure $$\vec {\mu }_s$$ μ → s corresponding to the unique invariant measure for the flow of the associated linear equation is quasi-invariant under the nonlinear stochastic flow.

Source: Stochastic Partial Differential Equations Analysis and Computations

DOI: 10.1007/s40072-025-00407-7

Authors: Justin Forlano, Leonardo Tolomeo

Institutions: Maxwell Institute for Mathematical Sciences, Monash University, University of Edinburgh

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: HORIZON EUROPE European Research Council