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Zero‐viscosity limit of the linearized Navier‐Stokes equations for a compressible viscous fluid in the half‐plane
Author(s) -
Xin Zhouping,
Yanagisawa Taku
Publication year - 1999
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(199904)52:4<479::aid-cpa4>3.0.co;2-1
Subject(s) - mathematics , pointwise , mathematical analysis , navier–stokes equations , viscosity , zero (linguistics) , limit (mathematics) , non dimensionalization and scaling of the navier–stokes equations , compressibility , plane (geometry) , boundary value problem , viscous liquid , stokes flow , compressible flow , geometry , mechanics , physics , flow (mathematics) , thermodynamics , linguistics , philosophy
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. © 1999 John Wiley & Sons, Inc.