Paper Info
Title
Stability of Boundary Layers for the Nonisentropic Compressible Circularly Symmetric 2D Flow.
Abstract
In this paper, we study the asymptotic behavior of circularly symmetric solutions to the initial boundary value problem of the nonisentropic compressible Navier-Stokes equations in a two-dimensional exterior domain with impermeable boundary conditions when the viscosities and the heat conduction coefficient tend to zero at the same rate. By multiscale analysis, we obtain that away from the boundary the nonisentropic compressible viscous flow can be approximated by the corresponding inviscid flow, and near the boundary there are boundary layers for the angular velocity, density, and temperature in the leading order expansions of solutions, while the radial velocity and pressure do not have boundary layers in the leading order. The boundary layers of velocity and temperature are described by a nonlinear parabolic system. We prove the stability of boundary layers and rigorously justify the asymptotic behavior of solutions in the L8 space for the small viscosities and heat-conduction limit in the Lagrangian coordinates, as long as the strength of the boundary layers is suitably small. Finally, we show that the similar asymptotic behavior of the small viscosities and heat conduction limit holds in the Eulerian coordinates for the compressible nonisentropic viscous flow.
Year
DOI
Venue
2014
10.1137/130906507
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
Field
DocType
boundary layers,thermal layers,compressible viscous flows,circularly symmetric,two space variables
Boundary value problem,Robin boundary condition,External flow,Mathematical optimization,No-slip condition,Boundary conditions in CFD,Boundary layer thickness,Mathematical analysis,Free boundary problem,Mathematics,Mixed boundary condition
Journal
Volume
Issue
ISSN
46
1
0036-1410
Citations 
PageRank 
References 
0
0.34
1
Authors
2
Name
Order
Citations
PageRank
Cheng-Jie Liu111.45
Yaguang Wang2296.70