Revista Matemática Iberoamericana

On the NLS dynamics for infinite energy vortex configurations on the plane

Fabrice Bethuel , Robert L. Jerrard , and Didier Smets

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Abstract

We derive the asymptotical dynamical law for Ginzburg-Landau vortices in the plane under the Schrödinger dynamics, as the Ginz\-burg-Landau parameter goes to zero. The limiting law is the well-known point-vortex system. This result extends to the whole plane previous results of [Colliander, J.E. and Jerrard, R.L.: Vortex dynamics for the Ginzburg-Landau-Schrödinger equation. Internat. Math. Res. Notices 1998, no. 7, 333-358; Lin, F.-H. and Xin, J.\,X.: On the incompressible fluid limit and the vortex motion law of the nonlinear Schr\"{o}dinger equation. Comm. Math. Phys. 200 (1999), 249-274] established for bounded domains, and holds for arbitrary degree at infinity. When this degree is non-zero, the total Ginzburg-Landau energy is infinite.

Article information

Source
Rev. Mat. Iberoamericana, Volume 24, Number 2 (2008), 671-702.

Dates
First available in Project Euclid: 11 August 2008

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1218475359

Mathematical Reviews number (MathSciNet)
MR2459209

Zentralblatt MATH identifier
1180.35045

Subjects
Primary: 35B20: Perturbations 35B40: Asymptotic behavior of solutions 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 82D50: Superfluids

Keywords
vortex dynamics NLS equation superfluids

Citation

Bethuel, Fabrice; Jerrard, Robert L.; Smets, Didier. On the NLS dynamics for infinite energy vortex configurations on the plane. Rev. Mat. Iberoamericana 24 (2008), no. 2, 671--702. https://projecteuclid.org/euclid.rmi/1218475359


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