Hydrodynamic Limit of the Gross-Pitaevskii Equation

Robert L. Jerrard, Daniel Spirn

Research output: Contribution to journalArticlepeer-review

6 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

Keywords

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

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