标题： 二维随机三次非线性波动方程的高斯测度的拟不变性 显示英文标题

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

摘要： 我们考虑二维环面$\mathbb T^2$上的随机阻尼非线性波动方程$\partial_t^{2}u+\partial_t u+u-\Delta u +u^{3} = \sqrt{2} {\langle{\nabla}\rangle^{-s}} \xi$，其中$\xi$表示一个时空白噪声，$s>0$。 我们证明了与相关线性方程流动的唯一不变测度对应的测度$\vec{\mu}_s$在非线性随机流动下是准不变的。 显示英文摘要

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