## Journal of Applied Mathematics

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

#### Abstract

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.

#### Article information

Source
J. Appl. Math., Volume 2014 (2014), Article ID 961014, 11 pages.

Dates
First available in Project Euclid: 2 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.jam/1425305907

Digital Object Identifier
doi:10.1155/2014/961014

Mathematical Reviews number (MathSciNet)
MR3240643

#### Citation

Lian, Ruxu; Hu, Liping. Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with a Nonconstant Exterior Pressure. J. Appl. Math. 2014 (2014), Article ID 961014, 11 pages. doi:10.1155/2014/961014. https://projecteuclid.org/euclid.jam/1425305907

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