Blow-up and Global Smooth Solutions for Incompressible Three-Dimensional Navier–Stokes Equations

2008 ◽  
Vol 25 (6) ◽  
pp. 2115-2117 ◽  
Author(s):  
Guo Bo-Ling ◽  
Yang Gan-Shan ◽  
Pu Xue-Ke
Keyword(s):  
Blow Up ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Smooth Solutions ◽  
Navier Stokes Equations ◽  
Global Smooth Solutions

Some stability results on global solutions to the Navier–Stokes equations

Analysis ◽  
2015 ◽  
Vol 35 (3) ◽  
Author(s):  
Isabelle Gallagher
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Global Solutions ◽  
Navier Stokes ◽  
Smooth Solutions ◽  
Navier Stokes Equations ◽  
Global Smooth Solutions ◽  
Whole Space ◽  
The Stability ◽  
Stability Results

AbstractIn these notes we present some results concerning the existence of global smooth solutions to the three-dimensional Navier–Stokes equations set in the whole space. We are particularly interested in the stability of the set of initial data giving rise to a global smooth solution.

BLOW-UP CRITERIA FOR THE NAVIER–STOKES EQUATIONS OF COMPRESSIBLE FLUIDS

2008 ◽  
Vol 05 (01) ◽  
pp. 167-185 ◽  
Author(s):  
JISHAN FAN ◽  
SONG JIANG
Keyword(s):  
Blow Up ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Compressible Fluids ◽  
Navier Stokes ◽  
Positive Density ◽  
Heat Conducting ◽  
Navier Stokes Equations ◽  
Local Strong Solutions

We study the Navier–Stokes equations of three-dimensional compressible isentropic and two-dimensional heat-conducting flows in a domain Ω with nonnegative density, which may vanish in an open subset (vacuum) of Ω, and with positive density, respectively. We prove some blow-up criteria for the local strong solutions.

BLOW-UP OF SMOOTH SOLUTIONS TO THE NAVIER–STOKES EQUATIONS OF COMPRESSIBLE VISCOUS HEAT-CONDUCTING FLUIDS

2010 ◽  
Vol 88 (2) ◽  
pp. 239-246 ◽  
Author(s):  
ZHONG TAN ◽  
YANJIN WANG
Keyword(s):  
Blow Up ◽  
Stokes Equations ◽  
Initial Density ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Smooth Solutions ◽  
Navier Stokes Equations ◽  
The Cauchy Problem ◽  
Heat Conducting Fluids ◽  
Conducting Fluids

AbstractWe give a simpler and refined proof of some blow-up results of smooth solutions to the Cauchy problem for the Navier–Stokes equations of compressible, viscous and heat-conducting fluids in arbitrary space dimensions. Our main results reveal that smooth solutions with compactly supported initial density will blow up in finite time, and that if the initial density decays at infinity in space, then there is no global solution for which the velocity decays as the reciprocal of the elapsed time.

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