The defocusing \(\dot{H}^{1/2}\)-critical NLS in high dimensions (Q379749)
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scientific article; zbMATH DE number 6224654
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The defocusing \(\dot{H}^{1/2}\)-critical NLS in high dimensions |
scientific article; zbMATH DE number 6224654 |
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The defocusing \(\dot{H}^{1/2}\)-critical NLS in high dimensions (English)
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11 November 2013
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The author proves conditional global existence and scattering (under a bound on the critical norm) of solutions of the defocusing \(\dot H^{\frac 12}\)-critical nonlinear Schrödinger equation in space dimensions greater than or equal to \(4\), extending the 3D result of Kenig and Merle. The proof follows the concentration-compactness/rigidity approach of Kenig and Merle, and uses a variant of the Morawetz inequality due to Lin and Strauss to prove the rigidity result.
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nonlinear Schrödinger equation
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critical space
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concentration-compactness
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global existence
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scattering
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