On nonlinear Schrödinger equations with repulsive inverse-power potentials

2018/12/20 by Dinh, Van Duong
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.08405

Abstract

In this paper, we consider the Cauchy problem for the nonlinear Schrödinger equations with repulsive inverse-power potentials i ∂_t u + Δu - c |x|^-σ u = ± |u|^αu, cgt;0. We study the local and global well-posedness, finite time blow-up and scattering in the energy space H¹ for the equation. These results extend a recent work of Miao-Zhang-Zheng [Nonlinear Schrödinger equation with coulomb potential, arXiv:1809.06685] to a general class of inverse-power potentials and higher dimensions.

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