Sharp blowup rate for NLS with a repulsive harmonic potential

Abstract

AbstractIn this paper, we are concerned with the blowup solutions of the $L^{2}$ L 2 critical nonlinear Schrödinger equation with a repulsive harmonic potential. By using the results recently obtained by Merle and Raphaël and by Carles’ transform we establish in a quite elementary way universal and sharp upper and lower bounds of the blowup rate for the blowup solutions of the aforementioned equation. As an application, we derive upper and lower bounds on the $L^{r}$ L r -norms of the singular solutions.