Regularity criterion of weak solutions to the 3D Navier-Stokes equations via two velocity components

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Abstract

This paper is concerned with the regularity criterion of Leray-Hopf weak solutions to the 3D Navier-Stokes equations with respect to Serrin type condition on two velocity filed components. It is shown that the weak solution u = (u1, u2, u3) is regular on (0, T] if there exist two solution components, for example, u2 and u3, satisfying the condition∇ u2, ∇ u3 ∈ Lp1 (0, T ; Lq1 (R3)), for  frac(2, p1) + frac(3, q1) ≤ 2, frac(3, 2) < q1 ≤ ∞ . © 2007 Elsevier Inc. All rights reserved.

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Dong, B. Q., & Chen, Z. M. (2008). Regularity criterion of weak solutions to the 3D Navier-Stokes equations via two velocity components. Journal of Mathematical Analysis and Applications, 338(1), 1–10. https://doi.org/10.1016/j.jmaa.2007.05.003

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