Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity

Massimilano Gubinelli, Herbert Koch, Tadahiro Oh

Research output: Working paper

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.
Original languageEnglish
PublisherArXiv
Number of pages49
Publication statusPublished - 2018

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