Three-dimensional stochastic cubic nonlinear wave equation with almost space-time white noise
Three-dimensional stochastic cubic nonlinear wave equation with almost space-time white noise
复制标题
DOI：
10.1007/s40072-022-00237-x
复制
发表时间：
2021-06
期刊：
影响因子：
--
通讯作者：
Tadahiro Oh;Yuzhao Wang;Younes Zine
中科院分区：
文献类型：
--
作者：
Tadahiro Oh;Yuzhao Wang;Younes Zine
研究了三维环面上具有加性噪声的随机三次非线性波动方程。特别地，当噪声几乎是时空白噪声时，我们证明了(重整化的)SNLW的局部适定性。近年来，仿控微积分在Gubinelli等人的奇异SNLW适定性研究中起到了至关重要的作用。(含二次非线性的三维随机非线性波动方程的Paractroled方法，2018年，arxiv：1811.07808[math.ap])，oh等人.(聚焦-具有Hartree类型非线性的模型，2020。Arxiv：2009.03251[math.PR])和Bringmann(具有Hartree非线性的三维波动方程的不变Gibbs度量II：动力学，2020年，arxiv：2009.04616[math.ap])。然而，我们的方法并不依赖于超控微积分。取而代之的是，我们继续进行二阶展开，并使用多线性色散平滑来研究得到的余项方程。
We study the stochastic cubic nonlinear wave equation (SNLW) with an additive noise on the three-dimensional torus. In particular, we prove local well-posedness of the (renormalized) SNLW when the noise is almost a space-time white noise. In recent years, the paracontrolled calculus has played a crucial role in the well-posedness study of singular SNLW onby Gubinelli et al. (Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity, 2018, arXiv:1811.07808 [math.AP]), Oh et al. (Focusing-model with a Hartree-type nonlinearity, 2020. arXiv:2009.03251 [math.PR]), and Bringmann (Invariant Gibbs measures for the three-dimensional wave equation with a Hartree nonlinearity II: Dynamics, 2020, arXiv:2009.04616 [math.AP]). Our approach, however, does not rely on the paracontrolled calculus. We instead proceed with the second order expansion and study the resulting equation for the residual term, using multilinear dispersive smoothing.