Blow-up for the focusing energy critical nonlinear Schrödinger equation with confining harmonic potential

Xing Cheng; Yanfang Gao

Xing Cheng ; Yanfang Gao

Colloquium Mathematicae, Tome 135 (2014), p. 143-149 / Harvested from The Polish Digital Mathematics Library

Résumé

The focusing nonlinear Schrödinger equation (NLS) with confining harmonic potential $i \partial_{t} u + 1 / 2 Δ u - 1 / 2 | x | ² u = - {| u |}^{4 / (d - 2)} u, x \in ℝ^{d}$ , is considered. By modifying a variational technique, we shall give a sufficient condition under which the corresponding solution blows up.

Publié le : 2014-01-01

Zbl 1294.35133

EUDML-ID : urn:eudml:doc:284377

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     author = {Xing Cheng and Yanfang Gao},
     title = {Blow-up for the focusing energy critical nonlinear Schr\"odinger equation with confining harmonic potential},
     journal = {Colloquium Mathematicae},
     volume = {135},
     year = {2014},
     pages = {143-149},
     zbl = {1294.35133},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm134-1-7}
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Xing Cheng; Yanfang Gao. Blow-up for the focusing energy critical nonlinear Schrödinger equation with confining harmonic potential. Colloquium Mathematicae, Tome 135 (2014) pp. 143-149. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm134-1-7/