Pullback attractors for a class of extremal solutions of the 3D Navier-Stokes system |
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Authors: | OV Kapustyan |
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Institution: | a Kyiv National Taras Shevchenko University, Kyiv, Ukraine b Institute of Applied System Analysis, Kyiv, Ukraine c Universidad Miguel Hernandez de Elche, Centro de Investigación Operativa, Avda. Universidad s/n, Elche, Spain |
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Abstract: | In this paper we construct a dynamical process (in general, multivalued) generated by the set of solutions of an optimal control problem for the three-dimensional Navier-Stokes system. We prove the existence of a pullback attractor for such multivalued process. Also, we establish the existence of a uniform global attractor containing the pullback attractor. Moreover, under the unproved assumption that strong globally defined solutions of the three-dimensional Navier-Stokes system exist, which guaranties the existence of a global attractor for the corresponding multivalued semiflow, we show that the pullback attractor of the process coincides with the global attractor of the semiflow. |
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Keywords: | 3D Navier-Stokes system Non-autonomous systems Optimal problems Multivalued systems Multivalued processes Pullback attractor |
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