Two blow-up regimes for \(L^2\) (Q2837172)
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scientific article; zbMATH DE number 6186346
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two blow-up regimes for \(L^2\) |
scientific article; zbMATH DE number 6186346 |
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10 July 2013
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nonlinear Schrödinger equations
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self-similar blow-up
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log-log blow-up
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0.8712913
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0.86741877
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0.8642874
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0.86343884
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0.8633182
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0.8619511
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Two blow-up regimes for \(L^2\) (English)
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The authors study two different blow-up regimes for \(L^2\) supercritical Schrödinger equations. NEWLINENEWLINENEWLINEThe first one concerns the quintic NLS in dimension \(N\geq 2\). In this case, by studying the equation with radial initial conditions, the authors show that there can be a blow-up of log-log type on a sphere. This blow up mechanism is stable under radial perturbations. In a second time, the authors state a blow-up regime for some \(L^2\) supercritical equations, which is of self-similar type. This blow up mechanism is stable. In both cases, a description of the blow-up solutions near the singularity is given. NEWLINENEWLINENEWLINEAfter a pedagogical introduction and the presentation of the results, the authors give the main ideas of the proofs.
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