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

This paper studies the global behavior to 3*D* 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”.

Cite this paper

*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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