Regularity criteria of the incompressible Navier-Stokes equations via only one entry of velocity gradient

0505896 - ÚH 2020 RIV CH eng J - Journal Article
Guo, Z. - Li, Y. - Skalák, Zdeněk
Regularity criteria of the incompressible Navier-Stokes equations via only one entry of velocity gradient.
Journal of Mathematical Fluid Mechanics. Roč. 21, č. 3 (2019), č. článku 35. ISSN 1422-6928. E-ISSN 1422-6952
R&D Projects: GA ČR(CZ) GA18-09628S
Institutional support: RVO:67985874
Keywords : Navier-Stokes equations * regularity criteria * one entry of velocity gradient
OECD category: Fluids and plasma physics (including surface physics)
Impact factor: 0.970, year: 2019
Method of publishing: Limited access
https://link.springer.com/article/10.1007%2Fs00021-019-0441-6

In this paper we establish regularity conditions for the three dimensional incompressible Navier-Stokes equationsin terms of one entry of the velocity gradient tensor, say for example,∂3u3. We show that if∂3u3satisfies certain integrableconditions with respect to time and space variables in anisotropic Lebesgue spaces, then a Leray-Hopf weak solution isactually regular. The anisotropic Lebesgue space helps us to almost reach the Prodi-Serrin level 2 in certain special case.Moreover, regularity conditions on non-diagonal element of gradient tensor∂1u3are also established, which covers someprevious literature.
Permanent Link: http://hdl.handle.net/11104/0297521