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Abstract / Description of output
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 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 Φ34-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.
Original language | English |
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Pages (from-to) | 898-963 |
Number of pages | 66 |
Journal | Stochastics and Partial Differential Equations: Analysis and Computations |
Volume | 10 |
Issue number | 3 |
Early online date | 13 Apr 2022 |
DOIs | |
Publication status | Published - 30 Sept 2022 |
Keywords / Materials (for Non-textual outputs)
- Nonlinear wave equation
- Pathwise well-posedness
- Stochastic nonlinear wave equation
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ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations
1/03/15 → 29/02/20
Project: Research