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Zero-viscosity limit of the linearized Navier-Stokes equations for a compressible viscous fluid in the half-plane

✍ Scribed by Zhouping Xin; Taku Yanagisawa

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 620 KB
Volume: 52
Category: Article
ISSN: 0010-3640
DOI: 10.1002/(sici)1097-0312(199904)52:4<479::aid-cpa4>3.0.co;2-1

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✦ Synopsis

The zero-viscosity limit for an initial boundary value problem of the linearized Navier-Stokes equations of a compressible viscous fluid in the half-plane is studied. By means of the asymptotic analysis with multiple scales, we first construct an approximate solution of the linearized problem of the Navier-Stokes equations as the combination of inner and boundary expansions. Next, by carefully using the technique on energy methods, we show the pointwise estimates of the error term of the approximate solution, which readily yield the uniform stability result for the linearized Navier-Stokes solution in the zero-viscosity limit.

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