On local strong solutions to the three-dimensional nonhomogeneous Navier–Stokes equations with density-dependent viscosity and vacuum

2019 ◽  
Vol 46 ◽  
pp. 58-81
Author(s):  
Boqiang Lü ◽  
Sisi Song
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Density Dependent ◽  
Local Strong Solutions ◽  
Dependent Viscosity

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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