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

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DOI: 10.4236/apm.2013.31A023    2,853 Downloads   5,051 Views  

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”.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. M-Ali and A. Kamara, "Scattering of the Radial Focusing Mass-Supercritical and Energy-Subcritical Nonlinear Schrödinger Equation in 3D," Advances in Pure Mathematics, Vol. 3 No. 1A, 2013, pp. 164-171. doi: 10.4236/apm.2013.31A023.

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