Global dynamics for a class of inhomogeneous nonlinear Schr "odinger\n equations with potential

2019/09/27 by Van Duong Dinh, Dinh, Van Duong · 1 citation
Mathematics · #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.1909.12836

Abstract

We consider a class of L²-supercritical inhomogeneous nonlinear\nSchr "odinger equations with potential in three dimensions\n n i
partial_t u +
Delta u - V u =
pm |x|^-b |u|^
alpha u,
quad (t,x)
in\n
mathbbR
times
mathbbR³,\n n where 0<b<1 and \α>\(4-2b)/(3). In the focusing case, by adapting\nan argument of Dodson-Murphy, we first study the energy scattering below the\nground state for the equation with radially symmetric initial data. We then\nestablish blow-up criteria for the equation whose proof is based on an argument\nof Du-Wu-Zhang. In the defocusing case, we also prove the energy scattering for\nthe equation with radially symmetric initial data.\n

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