Free boundary value problem for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity

2013 ◽  
Vol 93 (9) ◽  
pp. 1895-1908
Author(s):  
Ruxu Lian ◽  
Zigao Chen
Keyword(s):  
Free Boundary ◽  
Boundary Value Problem ◽  
Stokes Equations ◽  
Boundary Value ◽  
Navier Stokes ◽  
Free Boundary Value Problem ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
The One ◽  
Dependent Viscosity

scholarly journals Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with a Nonconstant Exterior Pressure

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Ruxu Lian ◽  
Liping Hu
Keyword(s):  
Free Boundary ◽  
Boundary Value Problem ◽  
Stokes Equations ◽  
Boundary Value ◽  
Viscosity Coefficient ◽  
Navier Stokes ◽  
Free Boundary Value Problem ◽  
One Dimensional ◽  
Global Strong Solution ◽  
Dependent Viscosity

We consider the free boundary value problem (FBVP) for one-dimensional isentropic compressible Navier-Stokes (CNS) equations with density-dependent viscosity coefficient in the case that across the free surface stress tensor is balanced by a nonconstant exterior pressure. Under certain assumptions imposed on the initial data and exterior pressure, we prove that there exists a unique global strong solution which is strictly positive from blow for any finite time and decays pointwise to zero at an algebraic time-rate.

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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