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

• 作者: Amadu Fullah Kamara Mujahid Abd Elmjed M-Ali
• 来源期刊: 理论数学进展(英文)
• 学科: 数学
• 关键词: NLS Blows-Up in Finite Time SUPREMUM Precompactness
• 年，卷（期）: 2013,（1）
• 页码范围: 164-171
• 页数: 8页
• 分类号: O1

摘要

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”.