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2013 Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data
Ruxu Lian, Guojing Zhang
J. Appl. Math. 2013: 1-11 (2013). DOI: 10.1155/2013/505108

Abstract

We study the free boundary value problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient and discontinuous initial data in this paper. For piecewise regular initial density, we show that there exists a unique global piecewise regular solution, the interface separating the flow and vacuum state propagates along particle path and expands outwards at an algebraic time-rate, the flow density is strictly positive from blow for any finite time and decays pointwise to zero at an algebraic time-rate, and the jump discontinuity of density also decays at an algebraic time-rate as the time tends to infinity.

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Ruxu Lian. Guojing Zhang. "Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data." J. Appl. Math. 2013 1 - 11, 2013. https://doi.org/10.1155/2013/505108

Information

Published: 2013
First available in Project Euclid: 14 March 2014

zbMATH: 1271.35060
MathSciNet: MR3074327
Digital Object Identifier: 10.1155/2013/505108

Rights: Copyright © 2013 Hindawi

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