Abstract
Majorants of the fractal dimension and of the number of determining modes for unbounded sets, invariant with respect to operators of semigroups of classes 1 and 2, are obtained. They are computed for the Navier-Stokes equations (two- and three-dimensional) under the first boundary condition and under periodicity conditions in the spaces\(H_0 \subset \vec L_2 (\Omega )\) and\(H^1 \subset \vec W_2 {}^1(\Omega )\).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 163, pp. 105–129, 1987.
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Ladyzhenskaya, O.A. Estimates for the fractal dimension and the number of determining modes for invariant sets of dynamical systems. J Math Sci 49, 1186–1201 (1990). https://doi.org/10.1007/BF02208714
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DOI: https://doi.org/10.1007/BF02208714