scholarly journals Remark on compressible Navier–Stokes equations with density-dependent viscosity and discontinuous initial data

2008 ◽  
Vol 339 (2) ◽  
pp. 1413-1424
Author(s):  
Ting Zhang ◽  
Daoyuan Fang
Keyword(s):  
Initial Data ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Density Dependent ◽  
Discontinuous 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→+∞.

scholarly journals Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Ruxu Lian ◽  
Guojing Zhang
Keyword(s):  
Free Boundary ◽  
Initial Data ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Free Boundary Value Problem ◽  
Time Rate ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Discontinuous Initial Data ◽  
Dependent Viscosity

We study the free boundary value problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient and discontinuous initial data in this paper. For piecewise regular initial density, we show that there exists a unique global piecewise regular solution, the interface separating the flow and vacuum state propagates along particle path and expands outwards at an algebraic time-rate, the flow density is strictly positive from blow for any finite time and decays pointwise to zero at an algebraic time-rate, and the jump discontinuity of density also decays at an algebraic time-rate as the time tends to infinity.

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