A sharp scattering condition for focusing mass-subcritical nonlinear Schrödinger equation

Abstract

This article is concerned with time global behavior of solutions to focusing mass-subcritical nonlinear Schrödinger equation of power type with data in a critical homogeneous weighted $L^2$ space. We give a sharp sufficient condition for scattering by proving existence of a threshold solution which does not scatter at least for one time direction and of which initial data attains minimum value of a norm of the weighted $L^2$ space in all initial value of non-scattering solution. Unlike in the mass-critical or -supercritical case, ground state is not a threshold. This is an extension of previous author's result to the case where the exponent of nonlinearity is below so-called Strauss number. A main new ingredient is a stability estimate in a Lorenz-modified-Bezov type spacetime norm.

59 pages, 1 figure

References in corpus (2)

• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation
• On minimal non-scattering solution for focusing mass-subcritical nonlinear Schrödinger equation

Cited by in corpus (1)

• Two minimization problems on non-scattering solutions to mass-subcritical nonlinear Schrödinger equation