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

0480807 - ÚH 2019 RIV US eng J - Journal Article
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. E-ISSN 1096-0813
R&D Projects: GA ČR GA13-00522S
Grant - others:National Natural Science Foundation of China(CN) 11301394
Institutional support: RVO:67985874
Keywords : Navier Stokes equations * conditional regularity * regularity criteria * vorticity * Besov spaces * bony decomposition
OECD category: Fluids and plasma physics (including surface physics)
Impact factor: 1.188, year: 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.
Permanent Link: http://hdl.handle.net/11104/0281875