Anisotropic and Geometric Criteria for Interior Regularity of Weak Solutions to the 3D Navier—Stokes Equations

2001 ◽  
pp. 237-265 ◽  
Author(s):  
Jiří Neustupa ◽  
Patrick Penel
Keyword(s):  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Interior Regularity ◽  
Regularity Of Weak Solutions

REGULARITY OF WEAK SOLUTIONS FOR THE NAVIER–STOKES EQUATIONS IN THE CLASS L∞(BMO-1)

2012 ◽  
Vol 14 (03) ◽  
pp. 1250020 ◽  
Author(s):  
WENDONG WANG ◽  
ZHIFEI ZHANG
Keyword(s):  
Weak Solution ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Removable Singularity ◽  
Navier Stokes ◽  
Singularity Theorem ◽  
Navier Stokes Equations ◽  
Regularity Of Weak Solutions ◽  
Mild Assumption

We study the regularity of weak solution for the Navier–Stokes equations in the class L∞( BMO-1). It is proved that the weak solution in L∞( BMO-1) is regular if it satisfies a mild assumption on the vorticity direction, or it is axisymmetric. A removable singularity theorem in ∈ L∞( VMO-1) is also proved.

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