Hydrodynamic limits of the nonlinear Klein-Gordon equation

Chi Kun Lin*, Kung Chien Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


We perform the mathematical derivation of the compressible and incompressible Euler equations from the modulated nonlinear Klein-Gordon equation. Before the formation of singularities in the limit system, the nonrelativistic-semiclassical limit is shown to be the compressible Euler equations. If we further rescale the time variable, then in the semiclassical limit (the light speed kept fixed), the incompressible Euler equations are recovered. The proof involves the modulated energy introduced by Brenier (2000) [1].

Original languageEnglish
Pages (from-to)328-345
Number of pages18
JournalJournal des Mathematiques Pures et Appliquees
Issue number3
Publication statusPublished - Sept 2012
Externally publishedYes


  • Euler equations
  • Hydrodynamic limits
  • Klein-Gordon equation

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