How to Cite
Downloads
Métricas Alternativas
Dimensions
Abstract
Stokes equations, we study several topics related with the long time behavior of solutions of an abstract class of evolutions equations in a separable Hilbert space, which generalizes several models of fluids mechanic. In particular we study the existence and uniqueness of weak solutions, as well as the existence of a global attractor and the convergence of solutions to the associated steady solutions.
References
S. Chandrasekhar. Hydrodynamic and Hydromagnetic Stability, Oxford at the Clarendon Press, (1961).
A. C. Eringen. “Theory of micropolar fluids”, J. Math.Mech., 16, 1–8, (1966).
E. Fernández Cara, F. Guillén-González & M. A. Rojas-Medar. Una formulación abstracta para algunas ecuaciones de la mecánica de los fluidos incompresibles, 58o Semin´ario Brasileiro de analise, Campinas, S.P. (2003).
D. Haragus, Equations du type Navier-Stokes, Monografia matemática, No. 49, Universitatea de Vest Timisoana, (1994).
L. C. F. Ferreira & E. J. Villamizar-Roa, “On the Existence and Stability of Solutions for the Micropolar Fluids in exterior domains”, Math. Methods Appl. Sci., 30, No. 10,1185–1208, (2007).
J. L. Lions & E. Magenes, Probl`emes aux limites nonhomegenes et applications. I, II, VI. Dunod, Paris,(1968).
G. Lukaszewicz, Micropolar Fluids. Theory and Applications, Modelling and Simulation in Science, Engineering and Technology, Birk¨auser, Boston, Basel, Berlin, (1999).
G. Lucaszewicz, E. E. Ortega-Torres & M. A. Rojas-Medar, “Strong periodic solutions for a class of abstract evolutions equations”, Nonlinear Analysis, Theory and Aplications, 54 6, 1045–1056, (2003).
L. A. Medeiros & P. H. Rivera, Espa¸cos de Sobolev e equa¸c˜oes diferen¸c˜aes par¸c˜oes, Textos de M´etodos Matem´aticos, No. 9, UFRJ, (1975).
M. Milla–Miranda, Prolongaci´on de soluciones de ecuaciones diferenciales ordinarias, Notas UFRJ, 155–171, (1980).
J. Simon, “Compact Sets in the Space Lp(0, T ; B)”, Ann. Mat. Pura Appl., Serie IV, Vol. 146, p.p. 65–96 (1987).
J. Simon, Existencia de soluci´on del problema de Navier-Stokes con densidad variable, Lectures at the University of Sevilla, Spain, (1989).
T. Temam, Infinite Dimensional Dynamical System in Mechanics and Physics, Second Edition, Springer-Verlag, New York, (1997).
T. Temam, Navier-Stokes Equations (Revised Edition), North-Holland, (1979).
E. J. Villamizar-Roa & M. A. Rodr´ıguez-Bellido, “Global Existence and Exponential Estability for the Micropolar Fluid”, Mathematik and Physik ZAMP, 58, 1–20, (2007).
E. J. Villamizar-Roa, M. A. Rodr´ıguez-Bellido & M. A. Rojas-Medar, “Some Properties of a Class of Abstract Stationary Equations”, Nonlinear Analysis, Theory and Aplications, 64, 2203–2214, (2006).
E. J. Villamizar-Roa, M. A. Rodr´ıguez-Bellido & M. A. Rojas-Medar, “The Boussinesq System with Mixed nonsmooth Boundary Data”, C. R. Math. Acad. Sci. Paris, 343, No. 3, 191–196, (2006).
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Copyright (c) 2023 Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales