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Semi-analytical study of the Voinovs problem

Published online by Cambridge University Press:  07 March 2018

E. A. KARABUT ,
A. G. PETROV  and
E. N. ZHURAVLEVA
E. A. KARABUT
Affiliation:
Lavrentyev Institute of Hydrodynamics, 630090, Novosibirsk, Russia email: eakarabut@gmail.com Novosibirsk State University, 630090, Novosibirsk, Russia email: zhuravleva_e@mail.ru
A. G. PETROV
Affiliation:
Institute for Problems in Mechanics, 119526, Moscow, Russia email: petrovipmech@gmail.com
E. N. ZHURAVLEVA
Affiliation:
Lavrentyev Institute of Hydrodynamics, 630090, Novosibirsk, Russia email: eakarabut@gmail.com Novosibirsk State University, 630090, Novosibirsk, Russia email: zhuravleva_e@mail.ru
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Abstract

A problem from the class of unsteady plane flows of an ideal fluid with a free boundary is considered. A conformal mapping of the exterior of a unit circle onto the region occupied by the fluid is sought. The solution is constructed in the form of power series in time or Laurent series which are analytically continued with the use of Padé approximants and change of variables of a certain special type. The free boundary shape and the pressure and velocity distributions are found. Singularities of the solution are studied.

Keywords

Conformal mappingPade approximantfree boundary flowideal incompressible fluid
Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Issue 2 , April 2019 , pp. 298 - 337
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

†The study was supported by Russian Science Foundation, project no. 14-19-01633 at the Ishlinsky Institute for Problems in Mechanics RAS.

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