Blow-Up Criteria of Strong Solutions and Conditional Regularity of Weak Solutions for the Compressible Navier-Stokes Equations

2018 ◽  
pp. 2263-2324 ◽  
Author(s):  
Yongzhong Sun ◽  
Zhifei Zhang
Keyword(s):  
Weak Solutions ◽  
Blow Up ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
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.

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.

Temporal and spatial decays for the Navier–Stokes equations

2005 ◽  
Vol 135 (3) ◽  
pp. 461-478 ◽  
Author(s):  
Hyeong-Ohk Bae ◽  
Bum Ja Jin
Keyword(s):  
Decay Rate ◽  
Weak Solutions ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Decay Rates ◽  
Navier Stokes ◽  
Spatial Decay ◽  
Navier Stokes Equations ◽  
Temporal Decay ◽  
Temporal And Spatial

We obtain spatial and temporal decay rates of weak solutions of the Navier–Stokes equations, and for strong solutions. For the spatial decay rate of the weak solutions, the power of the weight given by He and Xin in 2001 does not exceed 3/2;. However, we show the power can be extended up to 5/2;.

Sign in / Sign up

Export Citation Format

Share Document