On large-time energy concentration in solutions to the Navier-Stokes equations in general domains

0364506 - ÚH 2012 RIV DE eng J - Journal Article
Skalák, Zdeněk
On large-time energy concentration in solutions to the Navier-Stokes equations in general domains.
ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik. Roč. 91, č. 9 (2011), s. 724-732. ISSN 0044-2267. E-ISSN 1521-4001
R&D Projects: GA AV ČR IAA100190905
Institutional research plan: CEZ:AV0Z20600510
Keywords : Navier-Stokes equations * large-time behavior * energy concentration
Subject RIV: BA - General Mathematics
Impact factor: 0.863, year: 2011

In the paper we describe the large time energy concentration in the frequency space which occurs in global weak solutions to the Navier-Stokes equations satisfying the strong energy inequality. The energy of exponentially decreasing solutions concentrates in a particular ring in the frequency space. The diameter of the ring is connected with the rate of the exponential decay. The energy of solutions decreasing at an algebraic rate concentrates asymptotically in arbitrarily small frequencies. The results hold for any turbulent solution and for any three-dimensional sufficiently smooth domain. In Appendix, we present some further results connected with energy concentration.
Permanent Link: http://hdl.handle.net/11104/0199975