Free boundary problem for one‐dimensional compressible Navier–Stokes equations with temperature‐dependent viscosity and heat conductivity

2021 ◽  
Author(s):  
Tuowei Chen ◽  
Yongqian Zhang
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Heat Conductivity ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Dependent Viscosity

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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