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On large-time energy concentration in solutions to the Navier-Stokes equations in general domains
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SYSNO ASEP 0364506 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On large-time energy concentration in solutions to the Navier-Stokes equations in general domains Author(s) Skalák, Zdeněk (UH-J) SAI, ORCID, RID Source Title ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik. - : Wiley - ISSN 0044-2267
Roč. 91, č. 9 (2011), s. 724-732Number of pages 9 s. Language eng - English Country DE - Germany Keywords Navier-Stokes equations ; large-time behavior ; energy concentration Subject RIV BA - General Mathematics R&D Projects IAA100190905 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z20600510 - UH-J (2005-2011) UT WOS 000295068600004 DOI 10.1002/zamm.200900399 Annotation 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. Workplace Institute of Hydrodynamics Contact Soňa Hnilicová, hnilicova@ih.cas.cz, Tel.: 233 109 003 Year of Publishing 2012
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