Free boundary value problem of one dimensional two-phase liquid-gas model

2012 ◽  
Vol 32 (1) ◽  
pp. 413-432
Author(s):  
Wang Zhen ◽  
Zhang Hui
Keyword(s):  
Free Boundary ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Free Boundary Value Problem ◽  
Two Phase ◽  
One Dimensional ◽  
Phase Liquid

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 On the smoothness of the free boundary in a nonlocal one-dimensional parabolic free boundary value problem

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Rossitza Semerdjieva
Keyword(s):  
Free Boundary ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Sufficient Condition ◽  
Free Boundary Value Problem ◽  
Necessary And Sufficient Condition ◽  
One Dimensional ◽  
Necessary And Sufficient ◽  
Infinite Differentiability ◽  
Differential Condition

AbstractWe consider one-dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. Results on Cm-smoothness of the free boundary are obtained. In particular, a necessary and sufficient condition for infinite differentiability of the free boundary is given.

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