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arXiv · 1110.0915

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

François Genoud
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Abstract

An inhomogeneous nonlinear Schrödinger 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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François Genoud. 2011-10-05. An inhomogeneous, $L^2$ critical, nonlinear Schrödinger equation. https://arxiv.org/abs/1110.0915

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