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

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.

arXiv admin note: substantial text overlap with arXiv:2110.12980, arXiv:2109.08840; text overlap with arXiv:2007.15968, arXiv:2108.06205, arXiv:2012.13887, arXiv:2012.14562

References in corpus (4)

• Minimal blow-up solutions to the mass-critical inhomogeneous NLS equation
• Minimal mass blow-up solutions for nonlinear Schrödinger equations with an inverse potential
• Remarks on minimal mass blow up solutions for a double power nonlinear Schrödinger equation
• Minimal mass blow up solutions for a double power nonlinear Schrödinger equation