Remarks on minimal mass blow up solutions for a double power nonlinear Schrödinger equation

Abstract

We consider the following nonlinear Schrödinger equation with double power nonlinearity \[ i\frac{\partial u}{\partial t}+Δu+|u|^{\frac{4}{N}}u+|u|^{p-1}u=0,\quad 1<p<1+\frac{4}{N} \] in ${\mathbb{R}}^N$. For $N=1,2,3$, Le Coz-Martel-Raphaël (2016) construct a minimal-mass blow-up solution. Moreover, the previous study derives blow-up rate of the blow-up solution. In this paper, we extend this result to the general dimension. Furthermore, we investigate the behaviour of the critical mass blow-up solution near the blow-up time.

arXiv admin note: substantial text overlap with arXiv:2012.13887; text overlap with arXiv:2007.15968

Cited by in corpus (1)

• Minimal mass blow-up solutions for nonlinear Schrödinger equations with a singular potential