Blowup rate for mass critical rotational nonlinear Schr\"odinger equations

TL;DR

This paper investigates the blowup rates of solutions to mass-critical rotating nonlinear Schrödinger equations, establishing a precise logarithmic blowup law and constructing minimal mass solutions with varied blowup behaviors.

Contribution

It proves the log-log blowup rate under spectral conditions and constructs minimal mass blowup solutions with different blowup rates, advancing understanding of blowup dynamics in critical NLS.

Findings

Proved the log-log blowup law for certain initial data

Constructed minimal mass blowup solutions with distinct blowup rates

Identified spectral conditions influencing blowup behavior

Abstract

We consider the blowup rate for blowup solutions to $L^2$-critical, focusing NLS with a harmonic potential and a rotation term. Under a suitable spectral condition we prove that there holds the "$\log$-$\log$ law" when the initial data is slightly above the ground state. We also construct minimal mass blowup solutions near the ground state level with distinct blowup rates.