Global regularity criterion for the Navier‐Stokes equations based on the direction of vorticity

2019 ◽  
Vol 42 (18) ◽  
pp. 7126-7134 ◽  
Author(s):  
Zujin Zhang ◽  
Weihua Wang ◽  
Yong Zhou
Keyword(s):  
Global Regularity ◽  
Stokes Equations ◽  
Regularity Criterion ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals Global Regularity Criterion for the 3D Incompressible Navier–Stokes Equations Involving the Velocity Partial Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
TianLi Li ◽  
Wen Wang
Keyword(s):  
Weak Solution ◽  
Partial Derivative ◽  
Weak Solutions ◽  
Global Regularity ◽  
Stokes Equations ◽  
Regularity Criterion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Embedded Technology

In this paper, we study the regularity of the weak solutions for the incompressible 3D Navier–Stokes equations with the partial derivative of the velocity. By the embedded technology, we prove that the weak solution u is regular on (0, T] if ∂ 3 u ∈ L p 0 , T ; L q R 3 with 2 / p + 3 / q = 70 / 37 + 15 / 37 q , 15 / 4 ≤ q ≤ ∞ , or 2 / p + 3 / q = 34 / 19 + 9 / 19 q , 9 / 4 ≤ q ≤ ∞ .

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