Pullback attractors for a class of extremal solutions of the 3D Navier-Stokes system

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:373

Article

Kapustyan, O. V.²  Kasyanov, P. O.³  Valero, J.¹ 

[1] Univ Miguel Hernandez Elche, Ctr Invest Operat, Elche, Spain

[2] Kyiv Natl Taras Shevchenko Univ, Kiev, Ukraine

[3] Inst Appl Syst Anal, Kiev, Ukraine

关键词: 3D Navier-Stokes system;    Non-autonomous systems;    Optimal problems;    Multivalued systems;    Multivalued processes;    Pullback attractor;   

DOI  :  10.1016/j.jmaa.2010.07.040

来源: Elsevier

【 摘 要 】

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. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free