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arXiv · 1811.07808

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

Massimiliano Gubinelli·Herbert Koch·Tadahiro Oh
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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.

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Massimiliano Gubinelli, Herbert Koch, Tadahiro Oh. 2021-06-22. Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity. https://arxiv.org/abs/1811.07808

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