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- Title
Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity.
- Authors
Gubinelli, Massimiliano; Koch, Herbert; Oh, Tadahiro
- Abstract
Using ideas from paracontrolled calculus, we prove local well-posedness of a renormalized version of the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity forced by an additive space-time white noise on a periodic domain. There are two new ingredients as compared to the parabolic setting. (i) In constructing stochastic objects, we have to carefully exploit dispersion at a multilinear level. (ii) We introduce novel random operators and leverage their regularity to overcome the lack of smoothing of usual paradifferential commutators.
- Subjects
NONLINEAR wave equations; WHITE noise; RANDOM operators; NONLINEAR theories; SPACETIME
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2024, Vol 26, Issue 3, p817
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/1294