Blowup Criteria for Full Compressible Navier-Stokes Equations with Vacuum State

【Author】

Yongfu WANG;Shan LI;School of Economic Mathematics, Southwestern University of Finance and Economics;Corresponding author. Business College, Sichuan University;

【Institution】

School of Economic Mathematics, Southwestern University of Finance and Economics;Corresponding author. Business College, Sichuan University;

【Abstract】

This paper deals with the global strong solution to the three-dimensional(3D)full compressible Navier-Stokes systems with vacuum. The authors provide a sufficient condition which requires that the Sobolev norm of the temperature and some norm of the divergence of the velocity are bounded, for the global regularity of strong solution to the 3D compressible Navier-Stokes equations. This result indicates that the divergence of velocity fields plays a dominant role in the blowup mechanism for the full compressible Navier-Stokes equations in three dimensions.

【Keywords】

Compressible Navier-Stokes equations;;Heat-conduction;;Blowup criterion;;Divergence of velocity

References

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Springer Journals Database

Total: 27 articles

  • [1] Yonggeun Cho;;Hyunseok Kim, Existence results for viscous polytropic fluids with vacuum, Journal of Differential Equations, 2006 (2)
  • [2] D. Hoff, Global Solutions of the Navier-Stokes Equations for Multidimensional Compressible Flow with Discontinuous Initial Data, Journal of Differential Equations, 1995 (1)
  • [3] Yongzhong Sun;;Chao Wang;;Zhifei Zhang, A Beale–Kato–Majda blow-up criterion for the 3-D compressible Navier–Stokes equations, Journal de mathématiques pures et appliquées, 2010 (1)
  • [4] Jishan Fan;;Song Jiang;;Yaobin Ou, A blow-up criterion for compressible viscous heat-conductive flows, Annales de l'Institut Henri Poincare / Analyse non lineaire, 2009 (1)

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