Ill-posedness of a quasilinear wave equation in two dimensions for data in $H^{7/4}$
Analysis of PDEs
2023-08-30 v2
Abstract
In this article, we study the ill-posedness of a quasilinear wave equation. It was shown by Tataru and Smith in 2005 that for any (or in our situation), the equation is well-posed in . We show a sharpness result by exhibiting a quasilinear wave equation and an initial data such that the Cauchy problem is ill-posed for in .
Cite
@article{arxiv.2107.03732,
title = {Ill-posedness of a quasilinear wave equation in two dimensions for data in $H^{7/4}$},
author = {Gaspard Ohlmann},
journal= {arXiv preprint arXiv:2107.03732},
year = {2023}
}