Abstract
Using ideas from paracontrolled calculus, we prove local wellposedness of a renormalized version of the threedimensional stochastic nonlinear wave equation with quadratic nonlinearity forced by an additive spacetime 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 language  English 

Publisher  ArXiv 
Number of pages  49 
Publication status  Published  2018 
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Tadahiro Oh
 School of Mathematics  Personal Chair of Dispersive Equations
Person: Academic: Research Active