Nonlinear evolutionary Schrödinger equation in the supercritical case

Sh. M. Nasibov

Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 3, pp. 427-437

Résumé

We prove that for some initial data, solutions of the Cauchy problem for the nonlinear Schrödinger equation in the supercritical case are destroyed after a finite time, the exact value of which can be estimated from above. Lower bounds are obtained for the rate of destruction of the solution in some norms. A set of initial data is identified for which the solution of the Cauchy problem for the nonlinear Schrödinger equation in the supercritical case exists globally.

Détail

Keywords: nonlinear evolutionary Schrödinger equation, Cauchy problem, solution blow-up, blow-up rate, interpolation inequality, global solvability.

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