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Sibirskii Zhurnal Industrial'noi Matematiki, 2014, Volume 17, Number 4, Pages 67–78 (Mi sjim860)  
This article is cited in 1 scientific paper (total in 1 paper)

Shear Hele-Shaw flows of a weakly compressible fluid

Yu. A. Mëdovaab, A. A. Chesnokovba

a Lavrent'ev Institute of Hydrodynamics SB RAS, 15 Lavrent'ev av., 630090 Novosibirsk
b Novosibirsk State University, 2 Pirogova st., 630090 Novosibirsk
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Abstract: We derive the integro-differential system of equations describing shear flows of a weakly compressible multicomponent fluid in a Hele-Shaw cell. The propagation velocities of nonlinear perturbations in the fluid are determined, and the characteristic form of the system is obtained. We formulate conditions for the hyperbolicity of the model that are necessary for a correct statement of the Cauchy problem. One-dimensional multilayered flows are considered, and the interpretation of the Saffman-Taylor instability in the framework of the two-layered fluid scheme is given.
Keywords: Hele-Shaw flow, barotropic fluid, shear flow, hyperbolicity, stability.
Received: 05.05.2014
English version:
Journal of Applied and Industrial Mathematics, 2015, Volume 9, Issue 1, Pages 88–97
DOI: https://doi.org/10.1134/S199047891501010X
Bibliographic databases:
Document Type: Article
UDC: 533.951+517.948
Language: Russian
Citation: Yu. A. Mëdova, A. A. Chesnokov, “Shear Hele-Shaw flows of a weakly compressible fluid”, Sib. Zh. Ind. Mat., 17:4 (2014), 67–78; J. Appl. Industr. Math., 9:1 (2015), 88–97
Citation in format AMSBIB
\Bibitem{MedChe14}
\by Yu.~A.~M\"edova, A.~A.~Chesnokov
\paper Shear Hele-Shaw flows of a~weakly compressible fluid
\jour Sib. Zh. Ind. Mat.
\yr 2014
\vol 17
\issue 4
\pages 67--78
\mathnet{http://mi.mathnet.ru/sjim860}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3364394}
\transl
\jour J. Appl. Industr. Math.
\yr 2015
\vol 9
\issue 1
\pages 88--97
\crossref{https://doi.org/10.1134/S199047891501010X}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский журнал индустриальной математики
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