scholarly journals A Regularity Criterion for the Navier-Stokes Equations in the Multiplier Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Xiang'ou Zhu
Keyword(s):  
Weak Solution ◽  
Pressure Gradient ◽  
Sobolev Spaces ◽  
Special Class ◽  
Regularity Condition ◽  
Stokes Equations ◽  
Regularity Criterion ◽  
Navier Stokes ◽  
Navier Stokes Equations

We exhibit a regularity condition concerning the pressure gradient for the Navier-Stokes equations in a special class. It is shown that if the pressure gradient belongs to , where is the multipliers between Sobolev spaces whose definition is given later for , then the Leray-Hopf weak solution to the Navier-Stokes equations is actually regular.

scholarly journals Remarks on the Regularity Criterion of the Navier-Stokes Equations with Nonlinear Damping

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Weihua Wang ◽  
Guopeng Zhou
Keyword(s):  
Weak Solution ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Nonlinear Damping ◽  
Navier Stokes ◽  
Navier Stokes Equations

This paper is concerned with the regularity criterion of weak solutions to the three-dimensional Navier-Stokes equations with nonlinear damping in critical weakLqspaces. It is proved that if the weak solution satisfies∫0T∇u1Lq,∞2q/2q-3+∇u2Lq,∞2q/2q-3/1+ln⁡e+∇uL22ds<∞,  q>3/2, then the weak solution of Navier-Stokes equations with nonlinear damping is regular on(0,T].

scholarly journals A Remark on the Regularity Criterion for the 3D Boussinesq Equations Involving the Pressure Gradient

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Zujin Zhang
Keyword(s):  
Pressure Gradient ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Boussinesq Equations ◽  
Regularity Criterion ◽  
Navier Stokes ◽  
Navier Stokes Equations

We consider the three-dimensional Boussinesq equations and obtain a regularity criterion involving the pressure gradient in the Morrey-Companato spaceMp,q. This extends and improves the result of Gala (Gala 2013) for the Navier-Stokes equations.

scholarly journals A Note on the Regularity Criterion of Weak Solutions of Navier-Stokes Equations in Lorentz Space

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Xunwu Yin
Keyword(s):  
Weak Solution ◽  
Weak Solutions ◽  
Lebesgue Space ◽  
Lorentz Space ◽  
Stokes Equations ◽  
Regularity Criterion ◽  
Horizontal Velocity ◽  
Navier Stokes ◽  
Navier Stokes Equations

This paper is concerned with the regularity of Leray weak solutions to the 3D Navier-Stokes equations in Lorentz space. It is proved that the weak solution is regular if the horizontal velocity denoted byũ=(u1,u2,0)satisfiesũ(x,t)∈Lq(0,T;Lp,∞(R3))  for  2/q+3/p=1,  3<p<∞.The result is obvious and improved that of Dong and Chen (2008) on the Lebesgue space.

scholarly journals Direction of vorticity and a new regularity criterion for the Navier-Stokes equations

2005 ◽  
Vol 46 (3) ◽  
pp. 309-316 ◽  
Author(s):  
Yong Zhou
Keyword(s):  
Weak Solution ◽  
Stokes Equations ◽  
Regularity Criterion ◽  
Navier Stokes ◽  
Navier Stokes Equations

AbstractIn this paper, we prove a new regularity criterion in terms of the direction of vorticity for the weak solution to 3-D incompressible Navier-Stokes equations. Under the framework of Constantin and Fefferman, a more relaxed regularity criterion in terms of the direction of vorticity is established.

scholarly journals A regularity criterion for the Navier-Stokes equations in terms of the pressure gradient

2014 ◽  
Vol 12 (7) ◽  
Author(s):  
Stefano Bosia ◽  
Monica Conti ◽  
Vittorino Pata
Keyword(s):  
Pressure Gradient ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Regularity Criterion ◽  
Navier Stokes ◽  
Navier Stokes Equations

AbstractThe incompressible three-dimensional Navier-Stokes equations are considered. A new regularity criterion for weak solutions is established in terms of the pressure gradient.

A REGULARITY CRITERION FOR THE NAVIER–STOKES EQUATIONS IN TERMS OF ONE DIRECTIONAL DERIVATIVE OF THE VELOCITY FIELD

2012 ◽  
Vol 10 (04) ◽  
pp. 373-380 ◽  
Author(s):  
ZHENGGUANG GUO ◽  
SADEK GALA
Keyword(s):  
Weak Solution ◽  
Velocity Field ◽  
Stokes Equations ◽  
Directional Derivative ◽  
Regularity Criterion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Multiplier Space

We consider the regularity criterion for the incompressible Navier–Stokes equations. We show that the weak solution is regular, provided [Formula: see text] for some T > 0, where Ẋr is the multiplier space. This extends a result of Kukavica and Ziane [14].

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 ≤ ∞ .

Sign in / Sign up

Export Citation Format

Share Document