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 con...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”.展开更多
文摘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”.
