Abstract
The existence of global attractors is demonstrated for the dynamical systems generated by motions of nonlinear bipolar and non-Newtonian viscous fluids and upper bounds are obtained for the Hausdorff and fractal dimensions of the attractors for the bipolar case.
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Necas, J., and Silhavy, M. (1991). Multipolar viscous fluids.Q. Appl. Math. XLIX, 247–265.
Bellout, H., Bloom, F., and Necas, J. (1992). Phenomenological behavior of multipolar viscous fluids.Q. Appl. Math. L, 559–583.
Bellout, H., Bloom, F., and Necas, J. (1994). Young measure-valued solutions for non-Newtonian incompressible fluids.Comm. P.D.E. 19, 1763–1803.
Bellout, H., Bloom, F., and Necas, J. (1994). Existence, uniqueness, and stability of solutions to the initial boundary value problem for bipolar viscous fluids.Diff. Integral Eqs. 6, 513–542.
Ladyzhenskaya, O. (1965).The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York.
Ladyzhenskaya, O. (1970). New equations for the description of the viscous incompressible fluids and solvability in the large of the boundary value problems for them. InBoundary Value Problems of Mathematical Physics V, Am. Math. Soc., Providence, RI.
Necas, J. (1995). Fractal dimension of non-Newtonian attractors (in press).
Bellout, H., Bloom, F., and Necas, J. (1993). Weak and measure-valued solutions for non-Newtonian fluids.C.R. Acad. Sci. Paris 317, 795–800.
Bellout, H., Bloom, F., and Neas, J. (1995). Bounds for the dimensions of the attractors of nonlinear bipolar viscous fluids.Asymptot. Anal. (in press).
Ciarlet, P. G. (1987).Mathematical Elasticity, Vol. 1: Three-Dimensional Elasticity, North-Holland, Amsterdam.
Temam, R. (1988).Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York.
Constantin, P., and Foias, C. (1988).Navier-Stokes Equations, University of Chicago Press, Chicago.
Constantin, P., Foias, C., and Temam, R. (1985).Attractors Representing Turbulent Flows, Am. Math. Soc., Providence, RI.
Métivier, J. (1928). “Valeurs propres d'opérateurs définis sur la restriction de systèmes variationnels á des sous-espaces.J. Math. Pures Appl. 57, 133–156.
Ou, Y. R., and Sritharan, S. S. (1991). Analysis of regularized Navier-Stokes equations I.Quant. Appl. Math. XLIX, 651–685.
Ou, Y. R., and Sritharan, S. S. (1991). Analysis of regularized Navier-Stokes equations II.Quant. Appl. Math. XLIX, 687–728.
Sell, G. R., and Y. You, (1994). Dynamical Systems and Global Attractors, AH-PCRC Preprint 94-030, May, University of Minnesota, Minneapolis.
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Bloom, F. Attractors of non-Newtonian fluids. J Dyn Diff Equat 7, 109–140 (1995). https://doi.org/10.1007/BF02218816
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DOI: https://doi.org/10.1007/BF02218816