Hydrodynamic Limit of the Gross-Pitaevskii Equation

Robert L. Jerrard, Daniel Spirn

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We study dynamics of vortices in solutions of the Gross-Pitaevskii equation i∂tu = Δu + ϵ−2u(1 − |u|2) on ℝ2with nonzero degree at infinity. We prove that vortices move according to the classical Kirchhoff-Onsager ODE for a small but finite coupling parameter ϵ. 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].

Original languageEnglish (US)
Pages (from-to)135-190
Number of pages56
JournalCommunications in Partial Differential Equations
Volume40
Issue number2
DOIs
StatePublished - Feb 1 2015

Bibliographical note

Funding Information:
We are grateful to these agencies for their support. The first author was partially supported by the National Science and Engineering Research Council of Canada under operating grant 261955, and the second author was partially supported by NSF grant DMS-0955687.

Publisher Copyright:
© 2015, Taylor & Francis Group, LLC.

Keywords

  • Euler equations
  • Gross-Pitaevskii
  • Point vortex method
  • Vortices

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