Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity
arXiv:1811.07808
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.
52 pages. To appear in J. Eur. Math. Soc. Minor updates