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arXiv · 1903.03830

Global dynamics below the ground state for the focusing Schr\"odinger equation with a potential

Masaru Hamano·Masahiro Ikeda
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Abstract

In this paper, we consider the nonlinear Schr\"odinger 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".

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Masaru Hamano, Masahiro Ikeda. 2019-03-09. Global dynamics below the ground state for the focusing Schr\"odinger equation with a potential. https://arxiv.org/abs/1903.03830

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