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

DOI: 10.4236/apm.2013.31A023   PDF   HTML   XML   2,969 Downloads   5,256 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”.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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