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

We consider the stochastic damped nonlinear wave equation ∂ ₜ²u+∂ ₜ u+u-Δ u +u³ = √2 ∇ ⁻ˢ ξ ∂ t 2 u + ∂ t u + u - Δ u + u 3 = 2 ⟨ ∇ ⟩ - s ξ on the two-dimensional torus T² T 2 , where ξ ξ denotes a space-time white noise and $$s>0$$ s > 0 . We show that the measure μ ⃗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.