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Remarks on the regularity criterion of the 3D micropolar fluid flows in terms of the pressure. (English) Zbl 1210.35189

Summary: We study the regularity criterion of weak solutions to the three-dimensional (3D) micropolar fluid flows. It is proved that if the pressure satisfies

πL q (0,T;B p, r ( 3 )),2 q+3 p=2+r,3 2+r<p<,-1<r1,

then the weak solution (u,w) becomes a regular solution on (0,T]. The methods are based on the innovative function decomposition technique.

35Q35PDEs in connection with fluid mechanics
76W05Magnetohydrodynamics and electrohydrodynamics
35D30Weak solutions of PDE
35B65Smoothness and regularity of solutions of PDE
[1]Eringen, A.: Theory of micropolar fluids, J. math. Mech. 16, 1-18 (1966)
[2]Ladyzhenskaya, O.: The mathematical theory of viscous incompressible fluids, (1969) · Zbl 0184.52603
[3]Chen, J.; Dong, B. -Q.; Chen, Z. -M.: Uniform attractors of non-homogeneous micropolar fluid flows in non-smooth domains, Nonlinearity 20, 1619-1635 (2007) · Zbl 1155.37043 · doi:10.1088/0951-7715/20/7/005
[4]Dong, B. -Q.; Chen, Z. -M.: Asymptotic profiles of solutions to the 2D viscous incompressible micropolar fluid flows, Discrete contin. Dyn. syst. 23, 765-784 (2009) · Zbl 1170.35336 · doi:10.3934/dcds.2009.23.765
[5]Dong, B. -Q.; Zhang, Z.: Global regularity for the 2D micropolar fluid flows with zero angular viscosity, J. differential equations 249, 200-213 (2010)
[6]Galdi, G.; Rionero, S.: A note on the existence and uniqueness of solutions of micropolar fluid equations, Internat. J. Engrg. sci. 14, 105-108 (1977) · Zbl 0351.76006 · doi:10.1016/0020-7225(77)90025-8
[7]łukaszewicz, G.: Micropolar fluids. Theory and applications, Modeling and simulation in science, engineering and technology (1999)
[8]Dong, B. -Q.; Zhang, W.: On the regularity criterion for three-dimensional micropolar fluid flows in Besov spaces, Nonlinear anal. TMA 73, 2334-2341 (2010) · Zbl 1194.35322 · doi:10.1016/j.na.2010.06.029
[9]Dong, B. -Q.; Chen, Z. -M.: Regularity criteria of weak solutions to the three-dimensional micropolar flows, J. math. Phys. 50, 103525 (2009)
[10]Berselli, L.; Galdi, G.: Regularity criteria involving the pressure for the weak solutions to the Navier–Stokes equations, Proc. amer. Math. soc. 130, 3585-3595 (2002) · Zbl 1075.35031 · doi:10.1090/S0002-9939-02-06697-2
[11]Zhou, Y.: On regularity criteria in terms of pressure for the Navier–Stokes equations in R3, Proc. amer. Math. soc. 134, 149-156 (2006) · Zbl 1075.35044 · doi:10.1090/S0002-9939-05-08312-7
[12]Chen, Q.; Zhang, Z.: Regularity criterion via the pressure on weak solutions to the 3D Navier–Stokes equations, Proc. amer. Math. soc. 135, 1829-1837 (2007) · Zbl 1126.35047 · doi:10.1090/S0002-9939-06-08663-1
[13]B.-Q. Dong, Yan Jia, Z.-M. Chen, Pressure regularity criteria of the three-dimensional micropolar fluid flows, Math. Methods Appl. Sci., in press (doi:10.1002/mma.1383).
[14]Chemin, J. -Y.: Perfect incompressible fluids, (1998)
[15]Chen, Q.; Miao, C.; Zhang, Z.: On the uniqueness of weak solutions for the 3D Navier–Stokes equations, Ann. henri Poincaré 26, 2165-2180 (2009)
[16]Chen, Z. -M.; Price, W.: Decay estimates of linearized micropolar fluid flows in R3 space with applications to L3-strong solutions, Internat. J. Engrg. sci. 44, 859-873 (2006) · Zbl 1213.76012 · doi:10.1016/j.ijengsci.2006.06.003
[17]Kato, T.: Strong lp solutions of the Navier–Stokes equations in rm with applications to weak solutions, Math. Z. 187, 471-480 (1984) · Zbl 0545.35073 · doi:10.1007/BF01174182