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The continuation problem for the prandtl boundary layer

The continuation problem for the prandtl boundary layer Differential Equations, Vol. 36, No. 7, 2000, pp. 998-1002. Translated from Differentsial'nye Uravneniya, Vol. 36, No. 7, 2000, pp. 898-902. Original Russian Text Copyright (~ 2000 by Kuznetsov. PARTIAL DIFFERENTIAL EQUATIONS The Continuation Problem for the Prandtl Boundary Layer V. V. Kuznetsov Institute of Fluid Dynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, Russia Received February 11, 1999 The global solvability of the boundary value problem for the stationary Prandtl boundary layer was proved in [1-3] under various assumptions for the case in which the longitudinal gradient dp/dx of hydrodynamic pressure is nonpositive. In [4, 5], this result was generalized to the case in which the pressure can increase downstream and dp/dx has a special form (decreases by a power law for large x). The problem was most comprehensively investigated in [6]. If dp/dx >_ k > 0, then there necessarily exists a value x. of the longitudinal coordinate x for which the external flow adjoint to the boundary layer has a stagnation point, i.e., U (x.) = 0, where U is the velocity of the external (potential) motion. It was shown in [1] that in this case the boundary layer cannot be continued into the domain x > http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

The continuation problem for the prandtl boundary layer

Kuznetsov, V.
Differential Equations , Volume 36 (7) – Nov 15, 2007
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References (1)

Publisher
Springer Journals
Copyright
Copyright © 2000 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1007/BF02754500
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 36, No. 7, 2000, pp. 998-1002. Translated from Differentsial'nye Uravneniya, Vol. 36, No. 7, 2000, pp. 898-902. Original Russian Text Copyright (~ 2000 by Kuznetsov. PARTIAL DIFFERENTIAL EQUATIONS The Continuation Problem for the Prandtl Boundary Layer V. V. Kuznetsov Institute of Fluid Dynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, Russia Received February 11, 1999 The global solvability of the boundary value problem for the stationary Prandtl boundary layer was proved in [1-3] under various assumptions for the case in which the longitudinal gradient dp/dx of hydrodynamic pressure is nonpositive. In [4, 5], this result was generalized to the case in which the pressure can increase downstream and dp/dx has a special form (decreases by a power law for large x). The problem was most comprehensively investigated in [6]. If dp/dx >_ k > 0, then there necessarily exists a value x. of the longitudinal coordinate x for which the external flow adjoint to the boundary layer has a stagnation point, i.e., U (x.) = 0, where U is the velocity of the external (potential) motion. It was shown in [1] that in this case the boundary layer cannot be continued into the domain x >

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Differential Equations – Springer Journals

Published: Nov 15, 2007

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