On the regularity for solutions of the micropolar fluid equations

Elva Ortega-Torres; Marko Rojas-Medar

Rendiconti del Seminario Matematico della Università di Padova (2009)

  • Volume: 122, page 27-37
  • ISSN: 0041-8994

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Ortega-Torres, Elva, and Rojas-Medar, Marko. "On the regularity for solutions of the micropolar fluid equations." Rendiconti del Seminario Matematico della Università di Padova 122 (2009): 27-37. <http://eudml.org/doc/108774>.

@article{Ortega2009,
author = {Ortega-Torres, Elva, Rojas-Medar, Marko},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {27-37},
publisher = {Seminario Matematico of the University of Padua},
title = {On the regularity for solutions of the micropolar fluid equations},
url = {http://eudml.org/doc/108774},
volume = {122},
year = {2009},
}

TY - JOUR
AU - Ortega-Torres, Elva
AU - Rojas-Medar, Marko
TI - On the regularity for solutions of the micropolar fluid equations
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2009
PB - Seminario Matematico of the University of Padua
VL - 122
SP - 27
EP - 37
LA - eng
UR - http://eudml.org/doc/108774
ER -

References

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  1. [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. Zbl0837.35111
  2. [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. Zbl0927.35077MR1648218
  3. [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. Zbl0970.35105MR1765772
  4. [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. Zbl0601.35093MR876996
  5. [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. Zbl0940.35159MR1706110
  6. [6] D. CHAE- J. LEE, Regularity criterion intermsofpressure for theNavier-Stokes equations,NonlinearAnal.,46,no.5,Ser.A:TheoryMethods(2001),pp.727-735. Zbl1007.35064MR1857154
  7. [7] A. C. ERINGEN, Theory of micropolar fluids, J. Math. Mech., 16 (1966), pp. 1-8. MR204005
  8. [8] Y. GIYA - T. MIYAKAWA, Solutions in Lr to the Navier-Stokes initial value problem, Arch. Rat. Mech. Anal., 89 (1985), pp. 267-281. Zbl0587.35078MR786550
  9. [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. Zbl0808.35101MR1272655
  10. [10] S. KANIEL, A sufficient conditions for smoothness of solutions of NavierStokes equations, Israel J. Math., 6 (1968), pp. 354-358. Zbl0174.15003MR244651
  11. [11] S. KANIEL - M. SHINBROT, Smoothness of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 24 (1967), pp. 302-324. Zbl0152.44902MR214938
  12. [12] O. A. LADYZHENSKAYA, The mathematical theory of viscous incompressible flow, Second edition, Gordon and Breach (New York 1969). Zbl0184.52603MR254401
  13. [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. Zbl0692.76020MR1041744
  14. [14] G. LUKASZEWICZ, Micropolar fluids: theory and applications, Birkhäuser (Berlin 1998). Zbl0923.76003MR1711268
  15. [15] K. MASUDA, Weak solutions of Navier-Stokes equations, Tohoku Math. J., 36 (1984), pp. 623-646. Zbl0568.35077MR767409
  16. [16] M. O'LERAY, Pressure conditions for the local regularity of solutions of the Navier-Stokes equations, EJDE, 1998 (1998), pp. 1-9. Zbl0912.35123
  17. [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. Zbl0862.76097MR1413483
  18. [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. Zbl0918.35114MR1666509
  19. [19] J. SERRIN, On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Rat. Mech. Anal., 9 (1962), pp. 187-195. Zbl0106.18302MR136885
  20. [20] H. SOHR, The Navier-Stokes equations, a elementary functional analytic approach, Birkhäuser (Berlin 2001). Zbl0983.35004MR1928881
  21. [21] R. TEMAM, Navier-Stokes equations, theory and numerical analysis, North - Holland (2nd Revised Edition) (Amsterdam 1979). Zbl0426.35003MR603444
  22. [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. Zbl0451.35051MR566019
  23. [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. Zbl1078.35096MR2158216

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