Scattering of the Radial Focusing Mass-Supercritical and Energy-Subcritical Nonlinear Schrödinger Equation in 3D

Mujahid Abd Elmjed M-Ali, Amadu Fullah Kamara

Department of Mathematics, Faculty of Education, Kassala University, Kassala, Sudan.
Department of Mathematics, Faculty of Pure and Applied Sciences, Fourah Bay College, University of Sierra Leone, Freetown, Sierra Leone.

DOI: 10.4236/apm.2013.31A023                

Abstract

This paper studies the global behavior to 3D focusing nonlinear Schrodinger equation (NLS), the scaling index here is (0＜s_c＜1), which is the mass-supercritical and energy-subcritical, and we prove under some condition the solution u(t) is globally well-posed and scattered. We also show that the solution “blows-up in finite time” if the solution is not globally defined, as t→T we can provide a depiction of the behavior of the solution, where T is the “blow-up time”.

Keywords

NLS; Blows-Up in Finite Time; Supremum; Precompactness

Conflicts of Interest

The authors declare no conflicts of interest.

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