Advances in Pure Mathematics
Volume 3, Issue 1 (January 2013)
ISSN Print: 2160-0368 ISSN Online: 2160-0384
Google-based Impact Factor: 0.50 Citations h5-index & Ranking
Scattering of the Radial Focusing Mass-Supercritical and Energy-Subcritical Nonlinear Schrödinger Equation in 3D ()
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ABSTRACT
This paper studies the global behavior to 3D focusing nonlinear Schrodinger equation (NLS), the scaling index here is (0<sc<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”.
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