Hydrodynamic Limit of the Gross-Pitaevskii Equation |
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Authors: | Robert L. Jerrard |
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Affiliation: | Department of Mathematics , University of Toronto , Toronto , Canada |
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Abstract: | We study dynamics of vortices in solutions of the Gross-Pitaevskii equation i? t u = Δu + ??2 u(1 ? |u|2) on ?2 with nonzero degree at infinity. We prove that vortices move according to the classical Kirchhoff-Onsager ODE for a small but finite coupling parameter ?. By carefully tracking errors we allow for asymptotically large numbers of vortices, and this lets us connect the Gross-Pitaevskii equation on the plane to two dimensional incompressible Euler equations through the work of Schochet [19 Schochet , S. ( 1996 ). The point vortex method for periodic weak solutions of the 2D Euler equations . Comm. Pure Appl. Math. 49 : 911 – 965 .[Crossref], [Web of Science ®] , [Google Scholar]]. |
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Keywords: | Euler equations Gross-Pitaevskii Point vortex method Vortices |
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