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We study the stochastic cubic nonlinear wave equation (SNLW) with an additive noise on the three-dimensional torus 𝕋^3. 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 on 𝕋^3 by Gubinelli, Koch, and the first author (2018), Okamoto, Tolomeo, and the first author (2020), and Bringmann (2020). 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.
|Number of pages||66|
|Journal||Stochastics and Partial Differential Equations: Analysis and Computations|
|Early online date||13 Apr 2022|
|Publication status||E-pub ahead of print - 13 Apr 2022|
- stochastic nonlinear wave equation
- nonlinear wave equation
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1/03/20 → 28/02/25
1/03/15 → 29/02/20