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

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

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.

Date: 2013
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https://doi.org/10.1155/2013/505108

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:505108

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