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This is a Quantitative Study study.

October 18, 2025Open Access

Stochastic nonlinear wave equation with rougher than white noise

Key Points

Local well-posedness is established for stochastic wave equations with rough Matérn forcing.
The study expands existing results by considering rougher noise with α < 3/8.
New trilinear estimates in Bourgain spaces contribute to improved understanding of nonlinear effects.
This work strengthens earlier quadratic-case results showing local well-posedness with α < 1/2.

Abstract

We study the singular stochastic wave equation on T², with a cubic nonlinearity and Gaussian rough Matérn forcing (a Fourier multiplier of order α>0 applied to space-time white noise) and establish local well-posedness for α< 38. This extends GKO18 beyond white noise and strengthens the quadratic-case result OO21 (α< 12). Our argument develops new trilinear estimates in Bourgain spaces together with sharp, case-specific cubic counting estimates.

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Cite This Study

Li et al. (Tue,) studied this question.

synapsesocial.com/papers/68f408995de60f8893c6ffe7 https://doi.org/https://doi.org/10.48550/arxiv.2510.12221

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