A Phragmén–Lindelöf alternative result for the Navier–Stokes equations for steady compressible viscous flow

In this paper, the authors consider the Navier–Stokes equations for steady compressible viscous flow in three-dimensional cylindrical domain. A differential inequality for appropriate energy associated with the solutions of the Navier–Stokes isentropic flow in semi-infinite pipe is derived, from whi...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2008-04, Vol.340 (2), p.1480-1492
Main Authors: Lin, Changhao, Li, Haobin
Format: Article
Language:English
Subjects:
Decay estimates
Exact sciences and technology
Mathematical analysis
Mathematics
Navier–Stokes equations
Partial differential equations
Phragmén–Lindelöf alternative
Sciences and techniques of general use
Steady compressible viscous flow
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Summary:In this paper, the authors consider the Navier–Stokes equations for steady compressible viscous flow in three-dimensional cylindrical domain. A differential inequality for appropriate energy associated with the solutions of the Navier–Stokes isentropic flow in semi-infinite pipe is derived, from which the authors show a Phragmén–Lindelöf alternative result, i.e. the solutions for steady compressible viscous N–S flow problem either grow or decay exponentially as the distance from the entry section tends to infinity. In the decay case, the authors indicate how to bound explicitly the total energy in terms of data.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2007.09.037