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

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Author(s): Mujahid Abd Elmjed M-Ali | Amadu Fullah Kamara

Journal: Advances in Pure Mathematics
ISSN 2160-0368

Volume: 03;
Issue: 01;
Start page: 164;
Date: 2013;
Original page

Keywords: NLS | Blows-Up in Finite Time | Supremum | Precompactness

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 tT we can provide a depiction of the behavior of the solution, where T is the “blow-up time”.
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