An inhomogeneous, $L^2$ critical, nonlinear Schrödinger equation

Details An inhomogeneous, $L^2$ critical, nonlinear Schrödinger equation An inhomogeneous, $L^2$ critical, nonlinear Schrödinger equation

2011-10-05

arxiv.org/abs/1110.0915v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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