Nondispersive solutions to the mass critical half-wave equation in two dimensions
Analysis of PDEs
2020-07-31 v1
Abstract
We consider the half-wave equation with mass critical in two dimension \begin{eqnarray*} \begin{cases} iu_t=Du-|u|u,\,\,\, \\ u(0,x)=u_0(x), \end{cases} \end{eqnarray*} First, we prove the existence of a family of traveling solitary waves. We then show the existence of finite-time blowup solutions with minimal mass , where is the ground state solution of equation .
Keywords
Cite
@article{arxiv.2007.15370,
title = {Nondispersive solutions to the mass critical half-wave equation in two dimensions},
author = {Vladimir Georgiev and Yuan Li},
journal= {arXiv preprint arXiv:2007.15370},
year = {2020}
}