scholarly journals Well-posedness in critical spaces for the compressible Navier-Stokes equations with density dependent viscosities

2010 ◽  
pp. 915-946 ◽  
Author(s):  
Qionglei Chen ◽  
Changxing Miao ◽  
Zhifei Zhang
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Well Posedness ◽  
Critical Spaces ◽  
Navier Stokes Equations ◽  
Density Dependent

Density-dependent incompressible viscous fluids in critical spaces

2003 ◽  
Vol 133 (6) ◽  
pp. 1311-1334 ◽  
Author(s):  
R. Danchin
Keyword(s):  
Initial Velocity ◽  
Stokes Equations ◽  
Initial Density ◽  
Navier Stokes ◽  
Constant Density ◽  
Well Posedness ◽  
Critical Spaces ◽  
Density Dependent ◽  
Whole Space ◽  
Incompressible Viscous Fluids

We study the unique solvability of density-dependent incompressible Navier-Stokes equations in the whole space RN (N ≥ 2). The celebrated results by Fujita and Kato devoted to the constant density case are generalized to the case when the initial density is close to a constant: we find local well posedness for large initial velocity, and global well posedness for initial velocity small with respect to the viscosity. Our functional setting is very close to the one used by Fujita and Kato.

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