Interior regularity criterion via pressure on weak solutions to the Navier–Stokes equations

2007 ◽  
Vol 280 (1-2) ◽  
pp. 221-230 ◽  
Author(s):  
Tomoyuki Suzuki
Keyword(s):  
Weak Solutions ◽  
Stokes Equations ◽  
Regularity Criterion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Interior Regularity

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].

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