An inhomogeneous, \(L^2\)-critical, nonlinear Schrödinger equation (Q713222)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An inhomogeneous, \(L^2\)-critical, nonlinear Schrödinger equation |
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An inhomogeneous, \(L^2\)-critical, nonlinear Schrödinger equation (English)
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26 October 2012
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Summary: An inhomogeneous nonlinear Schrödinger equation is considered, which 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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global existence
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blow-up
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\(L^2\)-critical
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inhomogeneous NLS
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