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.

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.

Unique Strong Solutions and V -Attractors of a Three Dimensional System of Globally Modified Navier-Stokes Equations

2006 ◽  
Vol 6 (3) ◽  
Author(s):  
Tomás Caraballo ◽  
José Real ◽  
Peter E. Kloeden
Keyword(s):  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Dimensional System ◽  
Navier Stokes Equations ◽  
Three Dimensional System

AbstractWe prove the existence and uniqueness of strong solutions of a three dimensional system of globally modified Navier-Stokes equations. The flattening property is used to establish the existence of global V -attractors and a limiting argument is then used to obtain the existence of bounded entire weak solutions of the three dimensional Navier-Stokes equations with time independent forcing.

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