Universal Upper Bound on The Blowup Rate of Nonlinear Schr\"odinger Equation with Rotation

TL;DR

This paper establishes a universal upper limit on how quickly solutions to a rotating nonlinear Schrödinger equation can blow up, under specific symmetry and potential conditions, supported by numerical evidence.

Contribution

It provides the first universal upper bound on blowup rates for a class of nonlinear Schrödinger equations with rotation and trapping potential.

Findings

Universal upper bound on blowup rate proven mathematically.

Numerical simulations support the theoretical results.

Results apply to mass supercritical and energy subcritical regimes.

Abstract

In this paper, we prove a universal upper bound on the blowup rate of a focusing nonlinear Schr\"odinger equation with an angular momentum under a trapping harmonic potential, assuming that the initial data is radially symmetric in the weighted Sobolev space. The nonlinearity is in the mass supercritical and energy subcritical regime. Numerical simulations are also presented.