Global strong solutions for nonhomogeneous heat conducting Navier-Stokes equations

2017 ◽  
Vol 41 (1) ◽  
pp. 127-139 ◽  
Author(s):  
Xin Zhong
Keyword(s):  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Heat Conducting ◽  
Navier Stokes Equations ◽  
Global Strong Solutions ◽  
Nonhomogeneous Heat

ON THE ASYMPTOTIC ANALYSIS OF THE BGK MODEL TOWARD THE INCOMPRESSIBLE LINEAR NAVIER–STOKES EQUATION

2010 ◽  
Vol 20 (08) ◽  
pp. 1299-1318 ◽  
Author(s):  
A. BELLOUQUID
Keyword(s):  
Asymptotic Analysis ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Uniqueness Theorems ◽  
Bgk Model ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Stokes Systems ◽  
Global Strong Solutions

This paper deals with the analysis of the asymptotic limit for BGK model to the linearized Navier–Stokes equations when the Knudsen number ε tends to zero. The uniform (in ε) existence of global strong solutions and uniqueness theorems are proved for regular initial fluctuations. As ε tends to zero, the solution of BGK model converges strongly to the solution of the linearized Navier–Stokes systems. The validity of the BGK model is critically analyzed.

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.

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