A regularity criterion for the Navier-Stokes equations based on the gradient of one velocity component

0457499 - ÚH 2017 RIV US eng J - Journal Article
Skalák, Zdeněk
A regularity criterion for the Navier-Stokes equations based on the gradient of one velocity component.
Journal of Mathematical Analysis and Applications. Roč. 437, č. 1 (2016), s. 474-484. ISSN 0022-247X. E-ISSN 1096-0813
R&D Projects: GA ČR GA14-02067S
Institutional support: RVO:67985874
Keywords : Navier-Stokes equations * regularity of solutions * regularity criteria
OECD category: Fluids and plasma physics (including surface physics)
Impact factor: 1.064, year: 2016

We show that if uis a Leray solution to the Navier–Stokes equations in the full three-dimensional space with an initial condition from W^1,2 _0,σ, T>0and u ∈L^t (0, T; L^s), where 2/t +3/s =59/30for s ∈(2, 30/13]and 2/t +3/s =7/4 +1/(2s)for s ∈(30/13, 3)then uis regular on (0, T). We prove our result as a special case of a more general method which might possibly bring a further improvement.
Permanent Link: http://hdl.handle.net/11104/0258000