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Regular Papers

On the regularity criterion of strong solutions to the 3D Boussinesq equations

Pages 1829-1835 | Received 15 Jul 2010, Accepted 04 Oct 2010, Published online: 28 Jan 2011

References

  • Majda , A . 2003 . “ Introduction to PDEs and Waves for the Atmosphere and Ocean, ” . In Courant Lecture Notes in Mathematics , Vol. 9 , Providence, RI : AMS/CIMS .
  • Zhou , Y and Fan , J . 2010 . On the Cauchy problems for certain α-Boussinesq equations . Proc. R. Soc. Edinb. , 140A : 319 – 327 .
  • Cho , Y and Kim , H . 2004 . Unique solvability for the density-dependent Navier-Stokes equations . Nonlinear Anal. , 59 : 465 – 489 .
  • Leray , J . 1934 . Sur le mouvement d'un liquide visqueux emplissant l'espace . Acta Math. , 63 : 183 – 248 .
  • Hopf , E . 1951 . Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen . Math. Nachr. , 4 : 213 – 231 .
  • J. Serrin, The initial value problem for the Navier-Stokes equations, In Non-linear Problems, University of Wis-consin Press, Madison, WI, 1963, pp. 69–98 (Symposium Proceedings).
  • Prodi , G . 1959 . Un teorema di unicità per le equazioni di Navier-Stokes . Ann. Mat. Pura Appl. , 48 : 173 – 182 .
  • Struwe , M . 1988 . On partial regularity results for the Navier-Stokes equations . Commum. Pure Appl. Math. , 41 : 437 – 458 .
  • Escauriaza , L , Serëgin , GA and Sverak , V . 2003 . L 3,∞-solutions of Navier-Stokes equations and backward uniqueness . Usp. Mat. Nauk , 58 : 3 – 44 .
  • Beirão da Veiga , H . 1995 . A new regularity class for the Navier-Stokes equations in ℝ n . Chin. Ann. Math. , 16 : 407 – 412 .
  • Zhou , Y . 2005 . A new regularity criterion for the Navier-Stokes equations in terms of the direction of vorticity . Monatsh. Math. , 144 : 251 – 257 .
  • Zhou , Y . 2005 . Direction of vorticity and a new regularity criterion for the Navier-Stokes equations . ANZIAM J. , 46 : 309 – 316 .
  • Fan , J and Ozawa , T . 2009 . Regularity conditions for the 3D Boussinesq equations with partial viscosity terms . Nonlinearity , 22 : 553 – 568 .
  • Fan , J and Zhou , Y . 2009 . A note on regularity criterion for the 3D Boussinesq system with partial viscosity . Appl. Math. Lett. , 22 : 802 – 805 .
  • S. Gala, Remark on the regularity criterion on strong solutions to the 3D Boussinesq equations (Submitted).
  • H. Triebel, Interpolation Theory, Function Spaces, Differential Operators. North-Holland Mathematical Library, No. 18, North-Holland, Amsterdam, New York, 1978.
  • Chen , Z and Xin , Z . 2001 . Homogeneity criterion for the Navier-Stokes equations in the whole spaces . J. Math. Fluid Mech. , 3 : 152 – 182 .
  • Y. Meyer, P. Gerard and F. Oru, Inégalités de Sobolev précisées, Séminaire Équations aux dérivées partielles (Polytechnique), 1996–1997, Exp. No. 4, 8pp.
  • Ladyzhenskaya , O , Solonnikov , V and Ural'tseva , N . 1968 . “ Linear and Quasilinear Equations of Parabolic Type, ” . In Transactions of Mathematical Monographs , Vol. 23 , Providence, RI : American Mathematical Socity .

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