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

Authors

Justin Forlano, Leonardo Tolomeo

Published in

Stochastic partial differential equations : analysis and computations. Volume 14. Issue 2. Pages 830-876. Epub Dec 09, 2025.

Abstract

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

PMID:
42405360
Bibliographic data and abstract were imported from PubMed on 06 Jul 2026.

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