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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) v.22 n.1 Antofagasta mayo 2003

http://dx.doi.org/10.4067/S0716-09172003000100004 

Proyecciones
Vol. 22, N o 1, pp. 63-79, May 2003.
Universidad Católica del Norte
Antofagasta - Chile

STATIONARY SOLUTIONS OF
MAGNETO-MICROPOLAR FLUID
EQUATIONS IN EXTERIOR DOMAINS

M. DURÁN *
Pontificia Universidad Católica de Chile, Chile
E. ORTEGA-TORRES *
Universidad de Antofagasta, Chile
M. ROJAS-MEDAR
†
UNICAMP-IMECC, Brasil

Abstract

We establish the existence and uniqueness of the solution for the
magneto-micropolar fluid equations in the case of exterior domains in

IR 3 . First, we prove the existence of at least one weak solution of the
stationary system. Then we discuss its uniqueness.

 

Key Words: Magneto-Micropolar Fluid, Exterior domains, Nonlin-ear EDP

 

AMS Subject Classification: 35 Q35, 76 D05.

 

References

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[2] G. Ahmadi and M. Shahinpoor, Universal stability of magneto - micropolar fluid motions, Int. J. Enging Sci. 12, pp. 657-663, (1974).        [ Links ]

[3] E. V. Chizhonkov, On a system of equations of magnetohydrodynamic type, Soviet Math. Dokl. 30, pp. 542-545, (1984).        [ Links ]

[4] H. Fujita, On the existence and regularity of the steady-state solutions of the Navier-Stokes equations, J. Fac. Sci. Univ. Tokyo Sect. I, 9, pp. 59-102, (1981).        [ Links ]

[5] V. Girault and A.Sequeira, A well-posed problem for the exterior Stokes equations in two and three dimensions, Arch. Rational Mech. Anal. 114, pp. 313-333, (1991).        [ Links ]

[6] J. G. Heywood, On uniqueness questions in the theory of viscous flow, Acta Math. 136, pp. 61-102, (1976).        [ Links ]

[7] J. G. Heywood, The Navier-Stokes equations: on the existence, regularity and decay of solutions, Indiana Univ. Math. J. 29, pp. 639-681(1980).        [ Links ]

[8] O. A. Ladyszhenskaya, The mathematical theory of viscous incompressible flow, Second edition. Gordon and Breach, New York, (1969).        [ Links ]

[9] G. Lukaszewicz, On stationary flows of asymmetric fluids, Volume XII, Rend. Accad. Naz. Sci. detta dei XL, 106, pp. 35-44, (1988).        [ Links ]

[10] P. Galdi and S. Rionero, A note on the existence and uniqueness of solutions of the micropolar fluid equations, Int. J. Enging. Sci., 15, pp. 105-108, (1977).        [ Links ]

[11] M. Padula and R. Russo, A uniqueness theorem for micropolar fluid motions in unbounded regions, Bolletino U.M.I. (5) 13-A, pp. 660-666, (1976).        [ Links ]

Received : October 2002.

Mario Durán
Facultad de Ingeniería
Universidad Católica de Chile
Casilla 306
Correo 22
Santiago
Chile
e-mail : mduran@ing.puc.cl

Eliana Ortega-Torres
Departamento de Matemáticas
Universidad de Antofagasta
Casilla 170
Antofagasta
Chile
e-mail : eortega@uantof.cl

and

Marko Rojas-Medar
Departamento de Matemática Aplicada
UNICAMP - IMECC
CP 6065
13081-970
Campinas
Sao Paulo
Brasil
e-mail : marko@ime.unicamp.br

_______________

*Partially supported by Chilean Grant # 1000572 (FONDECYT).

†Partially supported by Brazilian Grant # 300116/93 (RN) (CNPq)

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