Stationary Solutions For Generalized Boussinesq Models In Exterior Domains

We establish the existence of a stationary weak solution of a generalized Boussinesq model for thermally driven convection in exterior domains. We use the fact that the exterior domain can be approximated by interior domains.199819Drazin, P.G., Reid, W.H., (1981) Hydrodynamic Stability, , Cambridge Univ. PressGilbarg, D., Trudinger, N.S., (1983) Elliptic Partial Differential Equations of Second Order, , Springer, Berlin-HeidelbergHeywood, J.G., The Navier-Stokes equations: On the existence, regularity and decay of solutions (1980) Indiana Univ. Math. J., 29, pp. 639-1181Heywood, J.G., On uniqueness questions in the theory of viscous flow (1976) Acta Math., 136, pp. 61-102Hishida, T., Asymptotic behavior and stability of solutions to exterior convection problem (1994) Nonlinear Anal., 22, pp. 895-925Korenev, N.K., On some problems of convection in a viscous incompressible fluid (1971) Vestnik Leningrad. Univ., (7)(1977) Vestnik Leningrad Univ. Math., 4, pp. 125-137. , English TransLadyzhenskaya, O.A., (1963) The Mathematical Theory of Viscous Incompressible Flow, , Gordon and Breach, New York-LondonLorca, S.A., Boldrini, J.L., Stationary solutions for Generalized Boussinesq models (1996) J. Diff. Eq., 124, pp. 389-406Lorca, S.A., Boldrini, J.L., The initial value Problem for generalized Boussinesq model Nonlinear Anal., , to appearMorimoto, H., On the existence and uniqueness of the stationary solution to the equations of natural convection (1991) Tokyo J. Math., 14, pp. 220-226Oeda, K., Stationary solutions of the heat convection equations in exterior domains (1997) Proc. Japan Acad., 73, pp. 111-115. , Ser. AOeda, K., Remarks on the periodic solution of the heat convection equation in a perturbed annulus domain (1997) Proc. Japan Acad., 73, pp. 21-25. , Ser. AOeda, K., Periodic solutions of the heat convection equation in exterior domain (1997) Proc. Japan Acad., 73, pp. 49-54. , Ser. ARojas-Medar, M.A., Lorca, S.A., The equations of a viscous incompressible chemical active fluid I: Uniqueness and existence of the local solutions (1995) Rev. Mat. Apl., 16, pp. 57-80Rojas-Medar, M.A., Lorca, S.A., The equations of a viscous incompressible chemical active fluid II: Regularity of solutions (1995) Rev. Mat. Apl., 16, pp. 81-9