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

0353112 - ÚH 2011 RIV CH eng J - Journal Article
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. E-ISSN 1422-6952
R&D Projects: GA AV ČR IAA200600801
Institutional research plan: CEZ:AV0Z20600510
Keywords : Navier–Stokes equations * asymptotic behavior of solution * fast decays
Subject RIV: BA - General Mathematics
Impact factor: 0.786, year: 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.
Permanent Link: http://hdl.handle.net/11104/0192443