Global well-posedness below the ground state for the nonlinear Schrödinger equation with a linear potential

Hamano, Masaru; Ikeda, Masahiro

doi:10.1090/proc/15161

Global well-posedness below the ground state for the nonlinear Schrödinger equation with a linear potential
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Proc. Amer. Math. Soc. 148 (2020), 5193-5207 Request permission

Abstract:

In this paper, we study existence of a standing wave solution for the nonlinear Schrödinger equation with a real-valued linear potential in energy-subcritical. Moreover, we also prove global well-posedness to the Cauchy problem with the initial data, whose action is less than that of the ground state with the potential. Hong [Commun. Pure Appl. Anal. 15 (2016), pp. 1571–1601] and the authors showed a scattering result for the problem with the initial data, whose action is less than that of the ground state without the potential. It was noted that the action of the ground state with the potential is greater than that of the ground state without the potential. Our new contribution enables us to treat initial data, which were not treated in those papers.

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