Communications in Mathematical Sciences

Asymptotic behavior of solutions to the full compressible Navier-Stokes equations in the half space

Feimin Huang, Jing Li, and Xiaoding Shi

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Abstract

The one-dimensional motion of compressible viscous and heat-conductive fluid is investigated in the half space. By examining the sign of fluid velocity prescribed on the boundary, initial boundary value problems with Dirichlet type boundary conditions are classified into three cases: impermeable wall problem, inflow problem and outflow problem. In this paper, the asymptotic stability of the rarefaction wave, boundary layer solution, and their combination is established for both the impermeable wall problem and the inflow problem under some smallness conditions. The proof is given by an elementary energy method.

Article information

Source
Commun. Math. Sci., Volume 8, Number 3 (2010), 639-654.

Dates
First available in Project Euclid: 25 August 2010

Permanent link to this document
https://projecteuclid.org/euclid.cms/1282747133

Mathematical Reviews number (MathSciNet)
MR2730324

Zentralblatt MATH identifier
1213.35101

Subjects
Primary: 35L65: Conservation laws

Keywords
Asymptotic behavior of solutions Navier-Stokes equations boundary layer rarefaction wave

Citation

Huang, Feimin; Li, Jing; Shi, Xiaoding. Asymptotic behavior of solutions to the full compressible Navier-Stokes equations in the half space. Commun. Math. Sci. 8 (2010), no. 3, 639--654. https://projecteuclid.org/euclid.cms/1282747133


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