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arXiv · 2510.12221

Stochastic nonlinear wave equation with rougher than white noise

Xue-Mei Li·Xianfeng Ren
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Abstract

We study the singular stochastic wave equation on $\mathbb T^2$, with a cubic nonlinearity and Gaussian rough Mat\'ern forcing (a Fourier multiplier of order $\alpha>0$ applied to space-time white noise) and establish local well-posedness for $\alpha < \tfrac{3}{8}$. This extends [GKO18] beyond white noise and strengthens the quadratic-case result [OO21] ($\alpha<\tfrac 12$). Our argument develops new trilinear estimates in Bourgain spaces together with sharp, case-specific cubic counting estimates.

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Xue-Mei Li, Xianfeng Ren. 2025-10-14. Stochastic nonlinear wave equation with rougher than white noise. https://arxiv.org/abs/2510.12221

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