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

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  • Ruxu Lian
  • Liping Hu

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.

Suggested Citation

  • Ruxu Lian & Liping Hu, 2014. "Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with a Nonconstant Exterior Pressure," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-11, July.
  • Handle: RePEc:hin:jnljam:961014
    DOI: 10.1155/2014/961014
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