Critical regularity criteria for Navier–Stokes equations in terms of one directional derivative of the velocity | Zendy

Chen Hui | Zendy; Fang Daoyuan | Zendy; Zhang Ting | Zendy

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Critical regularity criteria for Navier–Stokes equations in terms of one directional derivative of the velocity

Author(s) -

Chen Hui,

Fang Daoyuan,

Zhang Ting

Publication year - 2021

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.7097

Subject(s) - mathematics , a priori and a posteriori , rotational symmetry , navier–stokes equations , space (punctuation) , directional derivative , mathematical analysis , derivative (finance) , vector field , range (aeronautics) , field (mathematics) , material derivative , time derivative , geometry , compressibility , pure mathematics , mechanics , physics , financial economics , economics , philosophy , linguistics , materials science , epistemology , composite material

In this paper, we consider the 3D Navier–Stokes equations in the whole space. We investigate some new inequalities and a priori estimates to provide the critical regularity criteria in terms of one directional derivative of the velocity field, namely,∂ 3 u ∈ L p ( ( 0 , T ) ; L q ( ℝ 3 ) ) ,2 p + 3 q = 2 ,3 2 < q ≤ 6 . Moreover, we extend the range of q while the solution is axisymmetric, that is, the axisymmetric solution u is regular in (0, T ] , if∂ 3u 3 ∈ L p ( ( 0 , T ) ; L q ( ℝ 3 ) ) ,2 p + 3 q = 2 ,3 2 < q < ∞ .

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