On the stability of the Schwartz class under the magnetic Schr\"odinger flow

TL;DR

This paper proves that the Schwartz class of functions remains stable under the magnetic Schrödinger flow, given certain conditions on the magnetic field's non-degeneracy and behavior at infinity.

Contribution

It establishes the stability of the Schwartz class under magnetic Schrödinger flow with specific conditions on the magnetic 2-form, extending previous understanding.

Findings

Schwartz class remains stable under specified magnetic Schrödinger flow.

Stability depends on the magnetic 2-form being non-degenerate.

Limited oscillation of the magnetic field at infinity is required.

Abstract

We prove that the Schwartz class is stable under the magnetic Schr\"odinger flow when the magnetic $2$-form is non-degenerate and does not oscillate too much at infinity.