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Transactions of the Moscow Mathematical Society
Transactions of the Moscow Mathematical Society
ISSN 1547-738X(online) ISSN 0077-1554(print)

An axisymmetric boundary layer on a needle


Authors: A. D. Bryuno and T. V. Shadrina
Translated by: E. Khukhro
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 68 (2007).
Journal: Trans. Moscow Math. Soc. 2007, 201-259
MSC (2000): Primary 76D10, 76N20; Secondary 35B40, 34E05, 35A25, 35C20, 35Q30, 35Q35, 76D05, 80A20
Posted: November 15, 2007
MathSciNet review: 2429271
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Abstract | References | Similar Articles | Additional Information

Abstract: Methods of power geometry are used to study the boundary layer on a semi-infinite needle, due to a steady flow of a viscous fluid or gas parallel to the needle. The purpose is to find the asymptotics of the flow in the boundary layer at infinity along the needle. Two variants of the flow are considered: (a) an incompressible non-heat-conducting fluid, and (b) a compressible heat-conducting gas. It is shown that variant (a) has no asymptotics for solutions satisfying all the boundary conditions, whereas variant (b) has several families of asymptotics for solutions that satisfy all the boundary conditions. These asymptotic expansions have power or logarithmic singularities near the needle.


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Additional Information

A. D. Bryuno
Affiliation: Keldysh Institute of Applied Mathematics, Miusskaya pl. 4, Moscow 125047, Russia
Email: bruno@keldysh.ru

T. V. Shadrina
Affiliation: Keldysh Institute of Applied Mathematics, Miusskaya pl. 4, Moscow 125047, Russia
Email: shadrina@keldysh.ru

DOI: http://dx.doi.org/10.1090/S0077-1554-07-00165-3
PII: S 0077-1554(07)00165-3
Keywords: Boundary layer, asymptotics, Navier--Stokes equations, power geometry, incompressible viscous fluid, compressible gas
Posted: November 15, 2007
Additional Notes: This research was carried out with the support of the Russian Foundation for Basic Research (grant 05-01-00050).
Article copyright: © Copyright 2007 American Mathematical Society