Differential and Integral Equations

A remark on the Cauchy problem for the 2D Gross-Pitaevskii equation with nonzero degree at infinity

Fabrice Bethuel and Didier Smets

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We prove global well-posedness for the Gross-Pitaevskii equation on the plane for classes of initial data having nonzero topological degree at infinity and therefore infinite Ginzburg-Landau energy. These classes allow us to consider arbitrary configurations of vortices as initial data. Our work follows recent results of Patrick Gérard [9] and Clément Gallo [4], where the finite energy regime is treated.

Article information

Source
Differential Integral Equations Volume 20, Number 3 (2007), 325-338.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039505

Mathematical Reviews number (MathSciNet)
MR2293989

Zentralblatt MATH identifier
1212.35376

Subjects
Primary: 35Q40: PDEs in connection with quantum mechanics
Secondary: 35A05 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 47J30: Variational methods [See also 58Exx]

Citation

Bethuel, Fabrice; Smets, Didier. A remark on the Cauchy problem for the 2D Gross-Pitaevskii equation with nonzero degree at infinity. Differential Integral Equations 20 (2007), no. 3, 325--338. https://projecteuclid.org/euclid.die/1356039505.


Export citation