×
Ferreira, L. C. F.; Villamizar-Roa, E. J.

On the existence and stability of solutions for the micropolar fluids in exterior domains. (English) Zbl 1117.35065

Math. Methods Appl. Sci. 30, No. 10, 1185-1208 (2007).
Summary: We prove the existence of a global strong solution in some class of Marcinkiewicz spaces for the micropolar fluid in an exterior domain of \(\mathbb R^{3}\), with initial conditions being a non-smooth disturbance of a steady solution. We also analyse the large time behaviour of those solutions and apply our results in the context of the Navier-Stokes equations.

Cited in 6 Documents

MSC:

35Q35 PDEs in connection with fluid mechanics
76A05 Non-Newtonian fluids
35B40 Asymptotic behavior of solutions to PDEs

Keywords:

global strong solution; large time behaviour; asymptotic stability; Navier-Stokes equations
PDF BibTeX XML Cite
\textit{L. C. F. Ferreira} and \textit{E. J. Villamizar-Roa}, Math. Methods Appl. Sci. 30, No. 10, 1185--1208 (2007; Zbl 1117.35065)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Micropolar Fluids. Theory and Applications, Modeling and Simulation in Science, Engineering and Technology. Birkhauser: Boston, 1999.
[2] Eringen, Journal of Mathematics and Mechanics 16 pp 1– (1966)
[3] Durán, Proyecciones 22 pp 63– (2003)
[4] Lukaszewicz, Rendiconti della Accademia Nazionale delle Scienze detta dei XL Memorie di Matematica (5) 12 pp 83– (1988)
[5] Lukaszewicz, Rendiconti della Accademia Nazionale delle Scienze detta dei XL Memorie di Matematica (5) 13 pp 105– (1989)
[6] Ortega-Torres, Revista de Matematicas Aplicadas 17 pp 75– (1996)
[7] Rojas-Medar, Mathematische Nachrichten 188 pp 301– (1997)
[8] Rojas-Medar, Revista Matemática de la Universidad Complutense de Madrid 11 pp 443– (1998)
[9] Yamaguchi, Mathematical Methods in the Applied Sciences 28 pp 1507– (2005)
[10] Heywood, Indiana University Mathematics Journal 29 pp 639– (1980)
[11] Heywood, Archive for Rational Mechanics and Analysis 37 pp 48– (1970)
[12] Kozono, Archive for Rational Mechanics and Analysis 128 pp 1– (1994)
[13] Borchers, Acta Mathematica 174 pp 311– (1995)
[14] Kozono, Mathematische Zeitschrift 228 pp 751– (1998)
[15] Kozono, Mathematische Annalen 310 pp 279– (1998)
[16] Hishida, Journal of Differential Equations 141 pp 54– (1997) · Zbl 0905.35065
[17] Chen, Journal of Mathematical Analysis and Applications 181 pp 768– (1994)
[18] Fujiwara, Journal of Faculty of Science, University of Tokio, Section IA: Mathematics 24 pp 658– (1977)
[19] Giga, Mathematische Zeitschrift 178 pp 297– (1981)
[20] Equations of Evolution. Pitman: London, 1979.
[21] . Interpolation Spaces. Springer: Berlin, Heidelberg, New York, 1976.
[22] Hunt, L ’Enseignement Mathématique, t 12 pp 249– (1996)
[23] O’Neil, Duke Mathematical Journal 30 pp 129– (1963)
[24] Borchers, Acta Mathematica 165 pp 189– (1990)
[25] Kozono, Indiana University Mathematics Journal 41 pp 789– (1992)
[26] Barraza, Nonlinear Analysis 35 pp 747– (1999)
[27] Cannone, Journal of Mathematical and Fluid Mechanics 7 pp 1– (2005)
[28] Borchers, Mathematische Zeitschrift 196 pp 415– (1987)
[29] Recent Developments in the Navier–Stokes Problem. Chapman & Hall/CRC Press: Boca Raton, 2002. · Zbl 1034.35093
[30] Iwashita, Mathematische Annalen 285 pp 265– (1989)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.