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

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 i...

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Bibliographic Details
Published in:Journal of Applied Mathematics 2014-01, Vol.2014 (2014), p.860-870-977
Main Authors: Lian, Ruxu, Hu, Liping
Format: Article
Language:English
Subjects:
Aerodynamics
Aircraft
Algebra
Balancing
Boundary conditions
Boundary value problems
Compressibility
Decay
Electric power
Exteriors
Free boundaries
Mathematical analysis
Mathematical research
Navier-Stokes equations
Science
Studies
Viscosity
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Summary: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.
ISSN:1110-757X
1687-0042
DOI:10.1155/2014/961014