Global classical solution to the 3D isentropic compressible Navier-Stokes equations with general initial data and a density-dependent viscosity coefficient

2014 ◽  
Vol 38 (6) ◽  
pp. 1158-1177 ◽  
Author(s):  
Peixin Zhang
Keyword(s):  
Initial Data ◽  
Classical Solution ◽  
Stokes Equations ◽  
Viscosity Coefficient ◽  
Navier Stokes ◽  
Global Classical Solution ◽  
Navier Stokes Equations ◽  
Density Dependent ◽  
General Initial Data ◽  
Dependent Viscosity

scholarly journals Global Solutions to the Spherically Symmetric Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Ruxu Lian ◽  
Jianwei Yang ◽  
Jian Liu
Keyword(s):  
Initial Data ◽  
Regular Solution ◽  
Stokes Equations ◽  
Jump Discontinuity ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equations ◽  
Density Dependent ◽  
Discontinuous Initial Data ◽  
Dependent Viscosity

We consider the initial boundary value problem for the spherically symmetric isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficients and discontinuous initial data in this paper. For piecewise regular initial density with bounded jump discontinuity, we show that there exists a unique global piecewise regular solution. In particular, the jump of density decays exponentially in time and the piecewise regular solution tends to the equilibrium state exponentially ast→+∞.

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