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Scattering of the Radial Focusing Mass-Supercritical and Energy-Subcritical Nonlinear Schrödinger Equation in 3D
Department of Mathematics, Faculty of Education, Kassala University, Kassala, Sudan
Department of Mathematics, Faculty of Pure and Applied Sciences, Fourah Bay College, University of Sierra Leone, Freetown, Sierra Leone
- 1 Department of Mathematics, Faculty of Education, Kassala University, Kassala, Sudan
- 2 Department of Mathematics, Faculty of Pure and Applied Sciences, Fourah Bay College, University of Sierra Leone, Freetown, Sierra Leone
Advances in Pure Mathematics·Volume 03 (2013)·Pages 164–171·Published 30 January 2013·DOI10.4236/apm.2013.31A023
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Abstract
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”.
KeywordsNLSBlows-Up in Finite TimeSupremumPrecompactness
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