Journal of Applied Mathematics

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

Ruxu Lian and Guojing Zhang

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 505108, 11 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808047

Digital Object Identifier
doi:10.1155/2013/505108

Mathematical Reviews number (MathSciNet)
MR3074327

Zentralblatt MATH identifier
1271.35060

Citation

Lian, Ruxu; Zhang, Guojing. Free Boundary Value Problem for the One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data. J. Appl. Math. 2013 (2013), Article ID 505108, 11 pages. doi:10.1155/2013/505108. https://projecteuclid.org/euclid.jam/1394808047


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