Large Global Solutions for Nonlinear Schrodinger Equations II, Mass-Supercritical, Energy-Subcritical Cases

摘要

In this paper, we consider the defocusing mass-supercritical, energy-subcritical nonlinear Schrodinger equation, @@@ i partial derivative(t)u + Delta u = vertical bar u vertical bar(p)u, (t, x) is an element of Rd+1, @@@ with p is an element of (4/d, 4/d-2). We prove that under some restrictions on d, p, any radial function in the rough space H-s0 (R-d), for some s(0) < s(c) with the support away from the origin, there exists an incoming/outgoing decomposition, such that the initial data in the outgoing part leads to the global well-posedness and scattering forward in time; while the initial data in the incoming part leads to the global well-posedness and scattering backward in time. The proof is based on Phase-Space analysis of the nonlinear dynamics.

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