scholarly journals On the existence of global weak solutions to the Navier–Stokes equations for viscous compressible and heat conducting fluids

2007 ◽  
Vol 87 (1) ◽  
pp. 57-90 ◽  
Author(s):  
Didier Bresch ◽  
Benoît Desjardins
Keyword(s):  
Weak Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Global Weak Solutions ◽  
Navier Stokes Equations ◽  
Heat Conducting Fluids ◽  
Conducting Fluids

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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