Locally space-time anisotropic regularity criteria for the Navier–Stokes equations in terms of two vorticity components

0541483 - ÚH 2021 RIV CH eng J - Článek v odborném periodiku
Skalák, Zdeněk
Locally space-time anisotropic regularity criteria for the Navier–Stokes equations in terms of two vorticity components.
Journal of Mathematical Fluid Mechanics. Roč. 23, č. 2 (2021), č. článku 41. ISSN 1422-6928. E-ISSN 1422-6952
Grant CEP: GA ČR(CZ) GA18-09628S
Institucionální podpora: RVO:67985874
Klíčová slova: Navier-Stokes equations * regularity criterion * direction of vorticity
Obor OECD: Applied mathematics
Impakt faktor: 1.907, rok: 2021
Způsob publikování: Omezený přístup
https://link.springer.com/article/10.1007%2Fs00021-020-00544-0

In this paper we prove the regularity of Leray weak solutions of the Navier–Stokes equations as long as the vorticity projection to a plane is bounded in the scale critical space Lp(0,T,Lq), 2/p+3/q=2, q∈(3/2,∞). The plane may vary in space and time while the unit vector v=v(x,t) orthogonal to the plane is locally a Hölder function in space with the coefficient 1/2. This extends previous works by Chae and Choe and by Miller. We further show that a generalized form of this criterion improves several other regularity criteria in terms of the vorticity direction known from the literature.
Trvalý link: http://hdl.handle.net/11104/0319037