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

Massimiliano Gubinelli, Herbert Koch and Tadahiro Oh

First issued 19 November 2018 · PDF

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.

Versions

1. Version 3 (arXiv v3) current
   22 June 2021
   arXiv comments: 52 pages. To appear in J. Eur. Math. Soc. Minor updates
   PDF · LaTeX source · files and digests · arXiv:1811.07808
2. Version 2 (arXiv v2)
   24 March 2021
   arXiv comments: 52 pages. To appear in J. Eur. Math. Soc
   PDF · LaTeX source · files and digests · arXiv:1811.07808
3. Version 1 (arXiv v1)
   19 November 2018
   arXiv comments: 49 pages
   PDF · LaTeX source · files and digests · arXiv:1811.07808

Cite

Massimiliano Gubinelli, Herbert Koch and Tadahiro Oh. Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity. Papers of Massimiliano Gubinelli, 2018, version 3. https://mgubi.org/papers/paper/stochastic-wave-3d/

Licence: arXiv.org perpetual, non-exclusive license to distribute; all other rights reserved to the authors

Pin in the collection (SHA-512 of the inventory it fixes): 113f3bc9888bccc6df817615a39cb31bc92e4b61a2a97c5c7544de888f40d06f6f81e8eff3e1ab6bd5974ebdf6fbb336f0ba58da10043ef33a3335bdc6d7ff37

Papers of Massimiliano Gubinelli: an OpenSheaf archive (format 0.1, a draft); this page is generated by opensheaf-py from the archive.