English

Low regularity solutions to the stochastic geometric wave equation driven by a fractional Brownian sheet

Analysis of PDEs 2020-06-16 v1 Probability

Abstract

We announce a result on the existence of a unique local solution to a stochastic geometric wave equation on the one dimensional Minkowski space R1+1\mathbb{R}^{1+1} with values in an arbitrary compact Riemannian manifold. We consider a rough initial data in the sense that its regularity is lower than the energy critical.

Keywords

Cite

@article{arxiv.2006.07740,
  title  = {Low regularity solutions to the stochastic geometric wave equation driven by a fractional Brownian sheet},
  author = {Zdzisław Brzeźniak and Nimit Rana},
  journal= {arXiv preprint arXiv:2006.07740},
  year   = {2020}
}