Minimal mass blow-up solutions for nonlinear Schrödinger equations with a Hartree nonlinearity

2021/11/02 by Matsui, Naoki
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.08443

Abstract

We consider the following nonlinear Schrödinger equation with a Hartree nonlinearity: i(∂ u)/(∂ t)+Δu+|u|^(4)/(N)u±(\frac1|x|^2σ⋆|u|²)u=0 in ℝ^N. We are interested in the existence and behaviour of minimal mass blow-up solutions. Previous studies have shown the existence of minimal mass blow-up solutions with an inverse power potential and investigated the behaviour of the solution. In this paper, we investigate Hartree nonlinearity, which is a nonlinear term similar to the inverse power-type potential in terms of scaling.

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