English

Low regularity semi-linear wave equations

Analysis of PDEs 2016-09-07 v1

Abstract

We prove local well-posedness results for the semi-linear wave equation for data in HγH^\gamma, 0<γ<n32(n1)0 < \gamma < \frac{n-3}{2(n-1)}, extending the previously known results for this problem. The improvement comes from an introduction of a two-scale Lebesgue space Xkr,pX^{r,p}_k.

Keywords

Cite

@article{arxiv.math/9709222,
  title  = {Low regularity semi-linear wave equations},
  author = {Terence Tao},
  journal= {arXiv preprint arXiv:math/9709222},
  year   = {2016}
}