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Regularity criteria of weak solutions to the three-dimensional micropolar flows
J. Math. Phys. 50, 103525 (2009); doi:10.1063/1.3245862
Published 14 October 2009
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Regularity criteria of weak solutions to the three-dimensional micropolar fluid motion equations are discussed. Sufficient conditions for the regularity of weak solutions are presented by imposing Serrin's type growth conditions on the velocity field in Lorentz spaces, multiplier spaces, bounded mean oscillation spaces, and Besov spaces, respectively. The findings demonstrate that the velocity field plays a dominant role in the regularity problem of micropolar fluid motion equations.
©2009 American Institute of Physics
| History: | Received 14 May 2009; accepted 10 September 2009; published 14 October 2009 |
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- Beale, J., Kato, T., and Majda, A., “Remarks on the breakdown of smooth solutions for the 3-D Euler equations,”
Commun. Math. Phys. 94, 61 (1984) . - Beirão da Veiga, H., “A new regularity class for the Navier Stokes equations in Rn ,” Chin. Ann. Math., Ser. B 16, 407 (1995).
- Bergh, J. and Löfström, J., Interpolation Spaces (Springer, New York, 1976).
- Boldrini, J., Rojas-Medar, M. A., and Fernández-Cara, E., “Semi-Galerkin approximation and strong solutions to the equations of the nonhomogeneous asymmetric fluids,”
J. Math. Pures Appl. 82, 1499 (2003) . - Chemin, J. -Y., Perfect Incompressible Fluids (Oxford University Press, New York, 1998).
- Chen, Q., Miao, C., and Zhang, Z., “The Beale-Kato-Majda criterion for the 3D magneto-hydrodynamics equations,”
Commun. Math. Phys. 275, 861 (2007) . - Chen, Z. and Price, W., “Decay estimates of linearized micropolar fluid flows in R3 space with applications to L3-strong solutions,”
Int. J. Eng. Sci. 44, 859 (2006) . - Doi, M. and Edwards, S., The Theory of Polymer Dynamics (Oxford Science, Oxford, 1986).
- Dong, B. and Chen, Z., “Pressure regularity criteria of three-dimensional micropolar fluid flows” (unpublished).
- Eringen, A., “Theory of micropolar fluids,”
J. Math. Mech. 16, 1 (1966) . - Galdi, G. and Rionero, S., “A note on the existence and uniqueness of solutions of micropolar fluid equations,”
Int. J. Eng. Sci. 14, 105 (1977) . - Giga, Y., “Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system,”
J. Differ. Equations 62, 186 (1986) . - He, C. and Xin, X., “On the regularity of weak solutions to the magnetohydrodynamic equations,”
J. Differ. Equations 213, 235 (2005) . - Kozono, H., Ogawa, T., and Taniuchi, Y., “The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations,”
Math. Z. 242, 251 (2002) . - Kozono, H. and Taniuchi, Y., “Bilinear estimates in BMO and the Navier-Stokes equations,”
Math. Z. 235, 173 (2000) . - Ladyzhenskaya, O., The Mathematical Theory of Viscous Incompressible Fluids (Gordon and Breach, New York, 1969).
- Lemarié-Rieusset, P. G., Recent Developments in the Navier-Stokes Problem (Chapman Hall, London/CRC, Boca Raton, FL, 2002).
-
ukaszewicz, G., Micropolar Fluids. Theory and Applications, Modeling and Simulation in Science, Engineering and Technology (Birkhäuser, Boston, 1999). - Majda, A. and Bertozzi, A., Vorticity and Incompressible Flow (Cambridge University Press, Cambridge, 2002).
- Maz'ya, V., “On the theory of the n-dimensional Schrödinger operator,”
Izv. Akad. Nauk SSSR, Ser. Mat. 28, 1145 (1964) . - O'Neil, R., “Convolution operators and L(p,q) spaces,”
Duke Math. J. 30, 129 (1963) . - Popel, S., Regirer, A., and Usick, P., “A continuum model of blood flow,”
Biorheology 11, 427 (1974) . - Rojas-Medar, M., “Magneto-micropolar fluid motion: Existence and uniqueness of strong solution,”
Math. Nachr. 188, 301 (1997) . - Serrin, J., “On the interior regularity of weak solutions of the Navier Stokes equations,”
Arch. Ration. Mech. Anal. 9, 187 (1962) . - Stein, E., Harmonic Analysis: Real-Variable Methods Orthogonality, and Oscillatory Integrals (Princeton University Press, New Jersey, 1993).
- Struwe, M., “On partial regularity results for the Navier-Stokes equations,”
Commun. Pure Appl. Math. 41, 437 (1988) . - Triebel, H., Theory of Function Spaces (Birkhäuser, Boston, 1983).
- Zhou, Y., “Remarks on regularities for the 3D MHD equations,”
Discrete Contin. Dyn. Syst. 12, 881 (2005) . - Zhou, Y., “Regularity criteria for the 3D MHD equations in terms of the pressure,”
Int. J. Non-linear Mech. 41, 1174 (2006) . - Zhou, Y. and Gala, S., “Regularity criteria for the solutions to the 3D MHD equations in the multiplier space,” Z. Angew. Math. Phys. (to be published).
- Zhou, Y. and Gala, S., “On regularity criteria for the 3D micropolar fluid equations in the critical Morrey-Campanato space,” Preprint.
