On a Class of Nonlinear Schr\"{o}dinger Equations with Nonnegative Potentials in Two Space Dimensions

Jian Zhang ; Ji Shu

Matematičeskie zametki, Tome 91 (2012) no. 4, pp. 515-521.

Résumé

This paper discusses a class of critical nonlinear Schrödinger equations which are closely related to several applications, in particular to Bose-Einstein condensates with attractive two-body interactions. By constructing a constrained variational problem and considering the so-called invariant manifolds of the evolution flow, the authors derive a sharp criterion for blow-up and global existence of the solutions.

Détail

Keywords: nonlinear Schrödinger equation, blow-up, nonnegative potentials, constrained variational problem.
Mots-clés : global existence

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