TITLE:
Scattering of the Radial Focusing Mass-Supercritical and Energy-Subcritical Nonlinear Schrödinger Equation in 3D
AUTHORS:
Mujahid Abd Elmjed M-Ali, Amadu Fullah Kamara
KEYWORDS:
NLS; Blows-Up in Finite Time; Supremum; Precompactness
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.3 No.1A,
January
30,
2013
ABSTRACT:
This paper studies the global behavior to 3D focusing nonlinear Schrodinger equation (NLS), the scaling index here is (0sc1), 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”.