On the NLS dynamics for infinite energy vortex configurations on the plane
Fabrice
Bethuel
,
Robert L.
Jerrard
, and
Didier
Smets
Source: Rev. Mat. Iberoamericana
Volume 24, Number 2
(2008), 671-702.
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.
Primary Subjects: 35B20, 35B40, 35Q55, 82D50
Keywords: vortex dynamics; NLS equation; superfluids
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Permanent link to this document: http://projecteuclid.org/euclid.rmi/1218475359
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