English

Global well-posedness and scattering for the mass-critical Hartree equation with radial data

Analysis of PDEs 2009-01-11 v2 Mathematical Physics math.MP

Abstract

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Hartree equation iut+Δu=±(x2u2)uiu_t+\Delta u=\pm(|x|^{-2}*|u|^2)u for large spherically symmetric Lx2(Rd)L^2_x(\Bbb{R}^d) initial data; in the focusing case we require, of course, that the mass is strictly less than that of the ground state.

Keywords

Cite

@article{arxiv.0801.3925,
  title  = {Global well-posedness and scattering for the mass-critical Hartree equation with radial data},
  author = {Changxing Miao and Guixiang Xu and Lifeng Zhao},
  journal= {arXiv preprint arXiv:0801.3925},
  year   = {2009}
}

Comments

38 pages, 1 figure