Global Existence for a System of Weakly Coupled Nonlinear Schr\"{o}dinger Equations

Ji Shu ; Jian Zhang

Matematičeskie zametki, Tome 86 (2009) no. 5, pp. 686-691.

Résumé

This paper discusses the weakly coupled nonlinear Schrödinger equations in the supercritical case. With the best constant of Gagliardo–Nirenberg inequality, we derive a sufficient condition for the global existence of the solutions; this condition is expressed in terms of the stationary solutions (nonlinear ground state).

Détail

Keywords: weakly coupled nonlinear Schrödinger equations, Gagliardo–Nirenberg inequality, Cauchy problem, Laplace operator, nonlinear optics.
Mots-clés : global existence

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