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Remarques sur l'apparition de singularités dans les ecoulements euleriens compressible

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We recall some basic facts about the breakdown of smoothness in general hyperbolic systems and then, we prove that the breakdown of smoothness in an Euclidean flow comes from an accumulation of vorticity, divergence or compression.

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Bibliographie

  1. Beale, J.T., Kato, T., Majda, A.: Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Commun. Math. Phys.94, 61–66 (1984)

    Article  Google Scholar 

  2. Liu, T.P.: Development of singularities in the non-linear waves for quasi-linear hyperbolic partial differential equations. J. Diff. Eq.33, 92–111 (1979)

    Article  Google Scholar 

  3. Majda, A.: Compressible fluid flow and systems of conservation laws. Appl. Math. Sci.53 (1984)

  4. Makino, T., Ukai, S., Kawashima, S.: Sur la solution à support compact de l'équation d'Euler compressible. Jpn. J. Appl. Math.3, 249–257 (1986)

    Google Scholar 

  5. Ponce, G.: Remarks on a paper by J.T. Beale, T. Kato, and A. Majda. Commun. Math. Phys.98, 349–353 (1985)

    Article  Google Scholar 

  6. Sideris, T.: Formation of singularities in three dimensional compressible fluids. Commun. Math. Phys.101, 475–487 (1985)

    Article  Google Scholar 

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Communicated by T. Spencer

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Chemin, JY. Remarques sur l'apparition de singularités dans les ecoulements euleriens compressible. Commun.Math. Phys. 133, 323–329 (1990). https://doi.org/10.1007/BF02097370

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  • DOI: https://doi.org/10.1007/BF02097370

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