Journal d'Analyse Mathématique

, Volume 110, Issue 1, pp 297–338 | Cite as

On the linear wave regime of the Gross-Pitaevskii equation

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Abstract

We study long-wavelength asymptotics for the Gross-Pitaevskii equation corresponding to perturbations of a constant state of modulus one. We exhibit lower bounds on the first occurrence of possible zeros (vortices) and compare the solutions with the corresponding solutions to the linear wave equation or variants. The results rely on the use of the Madelung transform, which yields the hydrodynamical form of the Gross-Pitaevskii equation, as well as of an augmented system.

Keywords

Besov Space Strichartz Estimate Compressible Euler Equation Bernstein Inequality PITAEVSKII Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Hebrew University Magnes Press 2010

Authors and Affiliations

  • Fabrice Béthuel
    • 1
  • Raphaël Danchin
    • 2
  • Didier Smets
    • 1
  1. 1.Laboratoire J.-L. Lions UMR 7598Université Pierre et Marie CurieParisFrance
  2. 2.Lama, UMR 8050Université ParisestCréteil CedexFrance

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