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Sib. Èlektron. Mat. Izv., 2007, Volume 4, Pages 282–291 (Mi semr157)  

This article is cited in 1 scientific paper (total in 1 paper)

Research papers

Solvability of the initial boundary-value problems for hyperbolic model of ideal incompressible liquid motion

E. Yu. Meshcheryakova

M. A. Lavrent'ev Institute of Hydrodynamics

Abstract: We consider rotationally-symmetrical solutions to Euler equations with a linear dependence of axial component of velocity on axial coordinate. By methods of group analysis of differential equations these equations were reduced to one hyperbolic equation of the fourth order. For this equation a local in time unique solvability of initial boundary-value problem was proved. Also, for this equation a generalized Goursat problem was considered. There were formulated sufficient conditions of its solution non-existence and conditions of classical solution existence in case it is defined for all values of the radial coordinate. It is established that in the class of considered solutions to Euler equations, setting up initial velocity field in whole space does not determine the solution to Cauchy problem uniquely.

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Bibliographic databases:

Document Type: Article
UDC: 532.511, 517.9
MSC: 76B47
Received March 23, 2007, published June 29, 2007

Citation: E. Yu. Meshcheryakova, “Solvability of the initial boundary-value problems for hyperbolic model of ideal incompressible liquid motion”, Sib. Èlektron. Mat. Izv., 4 (2007), 282–291

Citation in format AMSBIB
\Bibitem{Mes07}
\by E.~Yu.~Meshcheryakova
\paper Solvability of the initial boundary-value problems for hyperbolic model of ideal incompressible liquid motion
\jour Sib. \`Elektron. Mat. Izv.
\yr 2007
\vol 4
\pages 282--291
\mathnet{http://mi.mathnet.ru/semr157}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2465427}
\zmath{https://zbmath.org/?q=an:1132.76302}


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    This publication is cited in the following articles:
    1. Meshcheryakova E.Yu., “Nonstationary Cylindrical Vortex in an Ideal Fluid”, J. Appl. Mech. Tech. Phys., 54:6 (2013), 921–927  crossref  mathscinet  zmath  isi  elib
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