Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data

Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data

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 s...

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Main Authors: Ruxu Lian, Guojing Zhang
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/505108
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spelling doaj-881e0f3161274a16857f83087ad0a6b42020-11-24T21:00:04ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/505108505108Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial DataRuxu Lian0Guojing Zhang1College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, ChinaSchool of Mathematics and Statistics, Northeast Normal University, Changchun 130024, ChinaWe 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.http://dx.doi.org/10.1155/2013/505108
collection DOAJ
language English
format Article
sources DOAJ
author Ruxu Lian
Guojing Zhang
spellingShingle Ruxu Lian
Guojing Zhang
Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data
Journal of Applied Mathematics
author_facet Ruxu Lian
Guojing Zhang
author_sort Ruxu Lian
title Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data
title_short Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data
title_full Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data
title_fullStr Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data
title_full_unstemmed Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data
title_sort free boundary value problem for the one-dimensional compressible navier-stokes equations with density-dependent viscosity and discontinuous initial data
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
description 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.
url http://dx.doi.org/10.1155/2013/505108
work_keys_str_mv AT ruxulian freeboundaryvalueproblemfortheonedimensionalcompressiblenavierstokesequationswithdensitydependentviscosityanddiscontinuousinitialdata
AT guojingzhang freeboundaryvalueproblemfortheonedimensionalcompressiblenavierstokesequationswithdensitydependentviscosityanddiscontinuousinitialdata
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