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

Naoki Matsui

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arXiv · 2111.08443

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

Naoki Matsui

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Abstract

We consider the following nonlinear Schrödinger equation with a Hartree nonlinearity: \[ i\frac{\partial u}{\partial t}+Δu+|u|^{\frac{4}{N}}u\pm\left(\frac{1}{|x|^{2σ}}\star|u|^2\right)u=0 \] in $\mathbb{R}^N$. 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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Naoki Matsui. 2021-11-02. Minimal mass blow-up solutions for nonlinear Schrödinger equations with a Hartree nonlinearity. https://arxiv.org/abs/2111.08443

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