An inhomogeneous, $L^2$ critical, nonlinear Schr\"odinger equation

François Genoud

An inhomogeneous, $L^2$ critical, nonlinear Schr\"odinger equation

Analysis of PDEs 2012-11-21 v1

Authors: François Genoud

Abstract

An inhomogeneous nonlinear Schr\"odinger equation is considered, that is invariant under $L^2$ scaling. The sharp condition for global existence of $H^1$ solutions is established, involving the $L^2$ norm of the ground state of the stationary equation. Strong instability of standing waves is proved by constructing self-similar solutions blowing up in finite time.

Keywords

inhomogeneous nonlinear Schrödinger equation $L^2$ critical global existence ground state standing waves strong instability self-similar solutions blow-up

Cite

@article{arxiv.1110.0915,
  title  = {An inhomogeneous, $L^2$ critical, nonlinear Schr\"odinger equation},
  author = {François Genoud},
  journal= {arXiv preprint arXiv:1110.0915},
  year   = {2012}
}

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