The energy space for the Gross-Pitaevskii equation with magnetic field

TL;DR

This paper investigates the conditions under which the energy space for the Gross-Pitaevskii equation with magnetic field is non-empty, providing a comprehensive characterization based on the magnetic field properties.

Contribution

It establishes necessary and sufficient conditions on the magnetic field for the energy space to be non-empty, advancing understanding of the equation's functional framework.

Findings

Identifies conditions on magnetic fields ensuring a non-empty energy space

Characterizes the energy space structure for the Gross-Pitaevskii equation with magnetic effects

Provides theoretical criteria relevant for mathematical and physical analysis

Abstract

We study the energy space for the Gross-Pitaevskii equation with magnetic field and non-vanishing conditions at infinity. We provide necessary and sufficient conditions on the magnetic field for which the energy space is non-empty.