×
Rojas-Medar, M. A.; Ortega-Torres, E. E.

The equations of a viscous asymmetric fluid: an interactive approach. (English) Zbl 1072.35568

ZAMM, Z. Angew. Math. Mech. 85, No. 7, 471-489 (2005).
Summary: We present a new proof of the existence and uniqueness of strong solutions for the equations of a viscous asymmetric fluid. We use an interactive approach and prove that the approximate solutions constructed by this method converge to a strong solution of these equations. We also give convergence-rate bounds for this method.

Cited in 12 Documents

MSC:

35Q35 PDEs in connection with fluid mechanics
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs

Keywords:

strong solution; convergence rates; a priori estimates; existence; uniqueness
PDF BibTeX XML Cite
\textit{M. A. Rojas-Medar} and \textit{E. E. Ortega-Torres}, ZAMM, Z. Angew. Math. Mech. 85, No. 7, 471--489 (2005; Zbl 1072.35568)
Full Text: DOI Link
  • logo of hbz
  • logo of WorldCat

References:

[1] Amrouche, Proc. Jpn. Acad. A, Math. Sci. (Japan) 67 pp 171– (1991) · Zbl 0752.35047
[2] Boldrini, Rev. Mat. Univ. Complutense Madr. 11(2) pp 443– (1998)
[3] Cattabriga, Rend. Sem. Univ. Padova 31 pp 308– (1961)
[4] Condiff, Phys. Fluids 7 pp 842– (1964)
[5] Eringen, J. Math. Mech. 16 pp 1– (1996)
[6] Eringen, Int. J. Eng. Sci. 2 pp 205– (1964)
[7] The Mathematical Theory of Viscous Incompressible Flow (Gordon and Breach, New York, London, Paris, 1969).
[8] and Linear and Quasi Linear Equations of Parabolic Type (AMS, Providence, R.I., 1968).
[9] Quelques Méthodes de Résolution de Problèmes aux Limites non Linéaires (Dunod, Paris, 1969).
[10] Lukaszewicz, Rend. Accad. Naz. Sci. XL, Mem. Math. 106(12) pp 83– (1988)
[11] Lukaszewicz, Rend. Accad. Naz. Sci. XL, Mem. Math. 106(13) pp 105– (1989)
[12] Micropolar Fluids, Theory and Applications (Birkhäuser, Boston, 1999).
[13] Ortega-Torres, Rev. Mat. Aplic. 17 pp 75– (1996)
[14] Ortega-Torres, Abs. Appl. Anal. 4 pp 109– (1999)
[15] Some Problems of Mechanics of Fluids with Antisymmetric Stress Tensor (Erevan, Armenia, 1984) (in Russian).
[16] Rojas-Medar, Math. Nachr. 188 pp 301– (1997)
[17] Rojas-Medar, Z. Angew. Math. Mech. 77(4) pp 1– (1997)
[18] Sedov, Differ. Uravn. (Russia) 16 pp 1114– (1980)
[19] Navier-Stokes Equations, Theory and Numerical Analysis, Rev. Ed. (North-Holland, Amsterdam, 1979). · Zbl 0426.35003
[20] Zarubin, Comput. Math. Phys. 33(8) pp 1077– (1993)
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.