JournalszaaVol. 31, No. 3pp. 283–290

An Inhomogeneous, L2L^2-Critical, Nonlinear Schrödinger Equation

  • François Genoud

    Heriot-Watt University, Edinburgh, UK
An Inhomogeneous, $L^2$-Critical, Nonlinear Schrödinger Equation cover
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Abstract

An inhomogeneous nonlinear Schrödinger equation is considered, which is invariant under L2L^2-scaling. The sharp condition for global existence of H1H^1-solutions is established, involving theL2L^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 fi nite time.

Cite this article

François Genoud, An Inhomogeneous, L2L^2-Critical, Nonlinear Schrödinger Equation. Z. Anal. Anwend. 31 (2012), no. 3, pp. 283–290

DOI 10.4171/ZAA/1460