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Global regularity of the 2D micropolar fluid flows with zero angular viscosity. (English) Zbl 1402.35220
Summary: We prove the global existence and uniqueness of smooth solutions to the 2D micropolar fluid flows with zero angular viscosity.

MSC:
35Q35 PDEs in connection with fluid mechanics
76S05 Flows in porous media; filtration; seepage
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35B65 Smoothness and regularity of solutions to PDEs
76A05 Non-Newtonian fluids
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
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[1] Beale, J.; Kato, T.; Majda, A., Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Comm. math. phys., 94, 61-66, (1984) · Zbl 0573.76029
[2] Bony, J.-M., Calcul symbolique et propagation des singularités pour LES équations aux dérivées partielles non linéaires, Ann. sci. école norm. sup., 14, 209-246, (1981) · Zbl 0495.35024
[3] Boldrini, J.; Rojas-Medar, M.A.; Fernández-Cara, E., Semi-Galerkin approximation and strong solutions to the equations of the nonhomogeneous asymmetric fluids, J. math. pures appl., 82, 1499-1525, (2003) · Zbl 1075.76005
[4] Cao, C.; Wu, J., Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion, (2009)
[5] Chae, D., Global regularity for the 2D Boussinesq equations with partial viscosity terms, Adv. math., 203, 497-513, (2006) · Zbl 1100.35084
[6] Chemin, J.-Y., Perfect incompressible fluids, (1998), Oxford University Press New York
[7] Chen, Z.; Price, W., Decay estimates of linearized micropolar fluid flows in \(\mathbb{R}^3\) space with applications to \(L_3\)-strong solutions, Internat. J. engrg. sci., 44, 859-873, (2006) · Zbl 1213.76012
[8] Conca, C.; Gormaz, R.; Ortega-Torres, E.; Rojas-Medar, M.A., The equations of non-homogeneous asymmetric fluids: an iterative approach, Math. methods appl. sci., 25, 1251-1280, (2002) · Zbl 1014.35079
[9] Constantin, P.; Masmoudi, N., Global well-posedness for a Smoluchowski equation coupled with navier – stokes equations in 2D, Comm. math. phys., 278, 179-191, (2008) · Zbl 1147.35069
[10] Dong, B.; Chen, Z., Asymptotic profiles of solutions to the 2D viscous incompressible micropolar fluid flows, Discrete contin. dyn. syst., 23, 765-784, (2009) · Zbl 1170.35336
[11] Eringen, A.C., Simple microfluids, Internat. J. engrg. sci., 2, 205-217, (1964) · Zbl 0136.45003
[12] Eringen, A.C., Theory of micropolar fluids, J. math. mech., 16, 1-18, (1966) · Zbl 0145.21302
[13] Ferrari, C., On lubrication with structured fluids, Appl. anal., 15, 127-146, (1983) · Zbl 0526.76006
[14] Galdi, G.P.; 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
[15] Hou, T.; Li, C., Global well-posedness of the viscous Boussinesq equations, Discrete contin. dyn. syst., 12, 1-12, (2005) · Zbl 1274.76185
[16] Kozono, H.; Taniuchi, Y., Limitting case of the Sobolev inequality in BMO with application to the Euler equations, Comm. math. phys., 214, 191-200, (2000) · Zbl 0985.46015
[17] Ladyzhenskaya, O.A., The mathematical theory of viscous incompressible fluids, (1969), Gorden Brech New York · Zbl 0184.52603
[18] Lin, F.-H.; Zhang, P.; Zhang, Z., On the global existence of smooth solution to the 2-d FENE dumbbell model, Comm. math. phys., 277, 531-553, (2008) · Zbl 1143.82035
[19] Łukaszewicz, G., Micropolar fluids. theory and applications, Model. simul. sci. eng. technol., (1999), Birkhäuser Boston · Zbl 0923.76003
[20] Masmoudi, N.; Zhang, P.; Zhang, Z., Global well-posedness for 2D polymeric fluid models and growth estimate, Phys. D, 237, 1663-1675, (2008) · Zbl 1143.76356
[21] Ortega-Torres, E.; Rojas-Medar, M.A., Magneto-micropolar fluid motion: global existence of strong solutions, Abstr. appl. anal., 4, 109-125, (1999) · Zbl 0976.35055
[22] Popel, S.; Regirer, A.; Usick, P., A continuum model of blood flow, Biorheology, 11, 427-437, (1974)
[23] Rojas-Medar, M.A., Magneto-micropolar fluid motion: existence and uniqueness of strong solution, Math. nachr., 188, 301-319, (1997) · Zbl 0893.76006
[24] Sastry, V.; Das, T., Stability of Couette fow and Dean fow in micropolar fluids, Internat. J. engrg. sci., 23, 1163-1177, (1985) · Zbl 0568.76013
[25] Temam, R., Navier – stokes equations, theory and numerical analysis, (1977), North-Holland Amsterdam, New York · Zbl 0383.35057
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