This article is cited in 2 papers

Nonlinear evolutionary Schrödinger equation in the supercritical case

Sh. M. Nasibov

Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan

Abstract: 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.

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

Received: 09.06.2021
Revised: 09.06.2021

DOI: 10.4213/tmf10134

 English version: Theoretical and Mathematical Physics, 2021, 209:3, 1683–1692

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