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Regularity criterion for solutions to the Navier-Stokes equations in the whole 3D space based on two vorticity components

  1. 1.
    0480807 - UH-J 2019 RIV US eng J - Článek v odborném periodiku
    Guo, Z. - Kučera, P. - Skalák, Zdeněk
    Regularity criterion for solutions to the Navier-Stokes equations in the whole 3D space based on two vorticity components.
    Journal of Mathematical Analysis and Applications. Roč. 458, č. 1 (2018), s. 755-766. ISSN 0022-247X
    Grant CEP: GA ČR GA13-00522S
    Grant ostatní:National Natural Science Foundation of China(CN) 11301394
    Institucionální podpora: RVO:67985874
    Klíčová slova: Navier Stokes equations * conditional regularity * regularity criteria * vorticity * Besov spaces * bony decomposition
    Kód oboru RIV: BA - Obecná matematika
    Obor OECD: Fluids and plasma physics (including surface physics)
    Impakt faktor: 1.188, rok: 2018

    We prove, among others, the following regularity criterion for the solutions to the Navier Stokes equations: If u is a global weak solution satisfying the energy inequality and omega = del x u, then u is regular on (0, T), T > 0, if two components of w belong to the space L-q (0, T, B-infinity infinity(-3/p)) for p is an element of (3, infinity) and 2/q + 3/p = 2. This result is an improvement of the results presented by Chae and Choe (1999) [7] or Zhang and Chen (2005) [38]. Our method of the proof uses a suitable application of the Bony decomposition and can also be used for the proofs of some other kin criteria. Otte such example is presented in Appendix. (C) 2017 Elsevier Inc. All rights reserved.
    Trvalý link: http://hdl.handle.net/11104/0281875