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On the Blow-up Criterion of 3D-NSE in Sobolev–Gevrey Spaces

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Abstract

In Benameur (Methods Appl 103:87–97, 2014), Benameur proved a blow-up result of the non regular solution of (NSE) in the Sobolev–Gevrey spaces. In this paper we improve this result, precisely we give an exponential type explosion in Sobolev–Gevrey spaces with less regularity on the initial condition. Fourier analysis and standard techniques are used.

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References

  1. Bahouri H., Chemin J.Y., Danchin R.: Fourier Analysis and Nonlinear Partial Differential Equations, pp. 343. Springer Verlag, Berlin (2011)

    Book  MATH  Google Scholar 

  2. Beale J., 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  ADS  MathSciNet  MATH  Google Scholar 

  3. Benameur J.: On the blow-up criterion of 3D Navier–Stokes equations. J. Math. Anal. Appl. 371(2), 719–727 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Benameur J.: On the blow-up criterion of the periodic incompressible fluids. Math. Methods Appl. Sci. 36(2), 143–153 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Benameur J.: On the exponential type explosion of Navier–Stokes equations. Nonlinear Anal. Theory Methods Appl. 103, 87–97 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cannone M.: Harmonic analysis tools for solving the incompressible Navier–Stokes equations. Diterot Editeur, Paris (1995)

    MATH  Google Scholar 

  7. Chemin, J.Y.: About Navier–Stokes Equations. Publication du Laboratoire Jaques-Louis Lions, Université de Paris VI, R96023 (1996)

  8. Foias C., Temam R.: Gevrey class regularity for the solutions of the Navier–Stokes equations. J. Funct. Anal. 87(2), 359–369 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  9. Leray J.: Essai sur le mouvement d’un liquide visqueux emplissant l’espace. Acta Math. 63, 22–25 (1933)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institut Supérieur des Sciences Appliquées, et Technologies de Gabès, Université de Gabès, Gabès, Tunisia

    Jamel Benameur

  2. Faculte de Sciences Mathematiques, Physiques et Naturelles de Tunis, Universite de Tunis El Manar, Tunis, Tunisia

    Lotfi Jlali

Authors
  1. Jamel Benameur
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  2. Lotfi Jlali
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Correspondence to Lotfi Jlali.

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Communicated by D. Chae

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Benameur, J., Jlali, L. On the Blow-up Criterion of 3D-NSE in Sobolev–Gevrey Spaces. J. Math. Fluid Mech. 18, 805–822 (2016). https://doi.org/10.1007/s00021-016-0263-8

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  • DOI: https://doi.org/10.1007/s00021-016-0263-8

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