Global dynamics below the ground state for the focusing Schrödinger equation with a potential
arXiv:1903.03830
Abstract
In this paper, we consider the nonlinear Schrödinger equation with a real valued potential V=V(x). We study global behavior of solutions to the equation with a data below the ground state under some conditions for the potential V and prove a scattering result and a blowing-up result in mass-supercritical and energy-subcritical. Our proof of the blowing-up or growing-up result without radially symmetric assumption is based on the argument by Du-Wu-Zhang in [6]. We can exclude the possibility of the growing-up result by the argument in [23], [15], and [10] if "the data and the potential are radially symmetric" or "the data has finite variance".
arXiv comment30 pages
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