On the regularity for solutions of the micropolar fluid equations
Rendiconti del Seminario Matematico della Università di Padova, Tome 122 (2009), pp. 27-37. 
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     author = {Ortega-Torres, Elva and Rojas-Medar, Marko},
     title = {On the regularity for solutions of the micropolar fluid equations},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {27--37},
     publisher = {Seminario Matematico of the University of Padua},
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     year = {2009},
     mrnumber = {2582828},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2009__122__27_0/}
}
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Ortega-Torres, Elva; Rojas-Medar, Marko. On the regularity for solutions of the micropolar fluid equations. Rendiconti del Seminario Matematico della Università di Padova, Tome 122 (2009), pp. 27-37. http://www.numdam.org/item/RSMUP_2009__122__27_0/

[1] H. Beirão Da Veiga, A new regularity class for the Navier-Stokes equations in Rn , Chin. Ann. of Math., 16B, 4 (1995), pp. 1-6. | Zbl

[2] H. Beirão Da Veiga, Concerning the regularity of the solutions to the NavierStokes equations via the truncation method Part II, In Equations aux dérivées partielles et applications Gauthier-Villars Éd. Sci. Méd. Elsevier (Paris 1998), pp. 127-138. | MR | Zbl

[3] H. Beirão Da Veiga, A Sufficient condition on the pressure for the regularity of weak Solutions to the Navier-Stokes equations, J. Math. Fluid Mech., 2 (2000), pp. 99-106. | MR | Zbl

[4] H. Beirão Da Veiga, Existence and asymptotic behavior for strong solutions of the Navier-Stokes equations in the whole space, Indiana Univ. Math. J., 36 (1987), pp. 149-166. | MR | Zbl

[5] L. Berselli, Sufficient conditions for the regularity of the solutions of the Navier-Stokes Equations, Math. Meth. Appl. Sci., 22 (1999), pp. 1079-1085. | MR | Zbl

[6] D. Chae- J. Lee, Regularity criterion intermsofpressure for theNavier-Stokes equations,NonlinearAnal.,46,no.5,Ser.A:TheoryMethods(2001),pp.727-735. | MR | Zbl

[7] A. C. Eringen, Theory of micropolar fluids, J. Math. Mech., 16 (1966), pp. 1-8. | MR

[8] Y. Giya - T. Miyakawa, Solutions in Lr to the Navier-Stokes initial value problem, Arch. Rat. Mech. Anal., 89 (1985), pp. 267-281. | MR | Zbl

[9] J. G. Heywood - O. D. Walsh, A counter-example concerning the pressure in the Navier-Stokes, as t 3 0‡ , Pacific J. Math., 164 (1994), pp. 351-359. | MR | Zbl

[10] S. Kaniel, A sufficient conditions for smoothness of solutions of NavierStokes equations, Israel J. Math., 6 (1968), pp. 354-358. | MR | Zbl

[11] S. Kaniel - M. Shinbrot, Smoothness of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 24 (1967), pp. 302-324. | MR | Zbl

[12] O. A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Second edition, Gordon and Breach (New York 1969). | MR | Zbl

[13] G. Lukaszewicz, On the existence, uniqueness and asymptotic properties of solutions of flows of asymmetric fluids, Rend. Accad. Naz. Sci. XL, Mem. Math., 107 (vol. XIII) (1989), pp. 105-120. | MR | Zbl

[14] G. Lukaszewicz, Micropolar fluids: theory and applications, Birkhäuser (Berlin 1998). | MR | Zbl

[15] K. Masuda, Weak solutions of Navier-Stokes equations, Tohoku Math. J., 36 (1984), pp. 623-646. | MR | Zbl

[16] M. O'Leray, Pressure conditions for the local regularity of solutions of the Navier-Stokes equations, EJDE, 1998 (1998), pp. 1-9. | Zbl

[17] E. Ortega-Torres - M. A. Rojas-Medar, On the uniqueness and regularity of the weak solutions for magneto-micropolar equations, Rev. Mat. Apl., 17 (1996), pp. 75-90. | MR | Zbl

[18] M. A. Rojas-Medar - J. L. Boldrini, Magneto-micropolar fluid motion: existence of weak solution, Rev. Mat. Univ. Complutense de Madrid., Vol. 11, 2 (1998), pp. 443-460. | MR | Zbl

[19] J. Serrin, On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Rat. Mech. Anal., 9 (1962), pp. 187-195. | MR | Zbl

[20] H. Sohr, The Navier-Stokes equations, a elementary functional analytic approach, Birkhäuser (Berlin 2001). | MR | Zbl

[21] R. Temam, Navier-Stokes equations, theory and numerical analysis, North - Holland (2nd Revised Edition) (Amsterdam 1979). | MR | Zbl

[22] W. Von Whalh, Regularity question for the Navier-Stokes equations, in: R. Rautmann ed., Approximations Methods for the Navier-Stokes Problems, Lectures and Notes in Mathematics, 771 (Springer-Verlag, Berlin 1980), pp. 538-542. | MR | Zbl

[23] N. Yamaguchi, Existence of global solution to the micropolar fluid system in a bounded domain, Math. Method Appl. Sci., 28 (2005), pp. 1507-1526. | MR | Zbl