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Some aspects of the asymptotic dynamics of solutions of the homogeneous Navier-Stokes equations in general domains

  1. 1.
    0353112 - UH-J 2011 RIV CH eng J - Článek v odborném periodiku
    Skalák, Zdeněk
    Some aspects of the asymptotic dynamics of solutions of the homogeneous Navier-Stokes equations in general domains.
    Journal of Mathematical Fluid Mechanics. Roč. 12, č. 4 (2010), s. 503-535 ISSN 1422-6928
    Grant CEP: GA AV ČR IAA200600801
    Výzkumný záměr: CEZ:AV0Z20600510
    Klíčová slova: Navier–Stokes equations * asymptotic behavior of solution * fast decays
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 0.786, rok: 2010

    In the first part of the paper we study decays of solutions of the Navier-Stokes equations on short time intervals. We show as the main result that solutions satisfying the strong energy inequality do not exhibit large decays if they are measured in the energetic L^2 norm. In the second part of the paper we characterize approximately the subspace of the phase space through which the trajectory of the solution moves. As a consequence of the presented results we get that the energy of solution cannot decay more quickly than exponentially.
    Trvalý link: http://hdl.handle.net/11104/0192443
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