scholarly journals Solvability of the free boundary value problem of the Navier-Stokes equations

2011 ◽  
Vol 29 (3) ◽  
pp. 769-801 ◽  
Author(s):  
Hantaek Bae ◽  
Keyword(s):  
Free Boundary ◽  
Boundary Value Problem ◽  
Stokes Equations ◽  
Boundary Value ◽  
Navier Stokes ◽  
Free Boundary Value Problem ◽  
Navier Stokes Equations

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.

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