Paper Info
Title
ZERO-VISCOSITY LIMIT OF THE LINEARIZED COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH HIGHLY OSCILLATORY FORCES IN THE HALF-PLANE
Abstract
We study the asymptotic behavior of the solution to the linearized compressible Navier - Stokes equations with highly oscillatory forces in the half-plane with nonslip boundary conditions for small viscosity. The wavelength of oscillation is assumed to be proportional to the square root of the viscosity. By means of asymptotic analysis, we deduce that the leading profiles of the solution have four terms: the first one is the outflow satisfying the linearized Euler equations, the second one is an oscillatory wave propagated along the characteristic field tangential to the boundary associated with the linearized Euler operator in the half-plane, the third one is a boundary layer satisfying a linearized Prandtl equation, the fourth one represents the oscillation propagated in the boundary layer, and it is described by an initial-boundary value problem for an Poisson - Prandtl coupled system. By using the energy method and mode analysis, we obtain the well-posedness of this Poisson - Prandtl coupled problem, and a rigorous theory on the asymptotic analysis of the zero-viscosity limit. Finally, we have briefly discussed the case that the wavelength of the oscillatoy force is shorter than the square root of the viscosity.
Year
DOI
Venue
2005
10.1137/040614967
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
Field
DocType
linearized compressible Navier-Stokes equations,boundary layers,oscillatory waves
Prandtl number,Boundary value problem,Mathematical optimization,Mathematical analysis,Euler operator,Boundary layer,Initial value problem,Compressible flow,Euler equations,Asymptotic analysis,Mathematics
Journal
Volume
Issue
ISSN
37
4
0036-1410
Citations 
PageRank 
References 
4
1.17
0
Authors
2
Name
Order
Citations
PageRank
Yaguang Wang1296.70
Zhouping Xin23011.22