Euler System for Perfect Incompressible Fluids

  • Hajer BahouriEmail author
  • Jean-Yves Chemin
  • Raphaël Danchin
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 343)


Chapter 7 is the natural continuation of the previous chapter: The diffusion term is removed, leading to the study of the Euler system for inviscid incompressible fluids. Here, we state local (in dimension d≥3) and global (in dimension two) well-posedness results for data in general Besov spaces. In particular, we study the case where the data belong to Besov spaces for which the embedding in the set of Lipschitz functions is critical. In the two-dimensional case, we also give results concerning the inviscid limit. We stress the case of data with (generalized) vortex patch structure.


Global Existence Smooth Solution Besov Space Euler System Inviscid Limit 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Hajer Bahouri
    • 1
    Email author
  • Jean-Yves Chemin
    • 2
  • Raphaël Danchin
    • 3
  1. 1.Départment de Mathématiques, Faculté des Sciences de Tunis, Campus UniversitaireUniversité de Tunis El ManarTunisTunisia
  2. 2.Laboratoire Jacques-Louis LionsUniversité Pierre et Marie CurieParis Cedex 05France
  3. 3.Centre de Mathématiques, Faculté de Sciences et TechnologieUniversité Paris XII-Val de MarneCréteil CedexFrance

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