Abstract:
This paper is devoted to the study of equations solution describing the axisymmetric motion of a viscous heat-conducting liquid. The motion is interpreted as a two-layer flow of viscous heat-conducting liquids in a cylinder with a solid wall and a common movable non-deformable interface. From a mathematical point of view, the arising initial-boundary value problem is nonlinear and inverse. Under certain assumptions concerning to apply the problem is replaced by a linear one. As a result, the unimprovable uniform priori estimates for solutions of the problems posed are obtained.
Keywords:
a priori estimates, the conjugate inverse problem, interface, Marangoni number.
Received: 28.02.2019 Received in revised form: 10.03.2019 Accepted: 12.06.2019
Bibliographic databases:
Document Type:
Article
UDC:
532.5.013.4
Language: English
Citation:
Victor K. Andreev, Evgeniy P. Magdenko, “A priori estimates of the conjugate problem describing an axisymmetric thermocapillary motion for small Marangoni number”, J. Sib. Fed. Univ. Math. Phys., 12:4 (2019), 483–495
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\by Victor~K.~Andreev, Evgeniy~P.~Magdenko
\paper A priori estimates of the conjugate problem describing an axisymmetric thermocapillary motion for small Marangoni number
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2019
\vol 12
\issue 4
\pages 483--495
\mathnet{http://mi.mathnet.ru/jsfu772}
\crossref{https://doi.org/10.17516/1997-1397-2019-12-4-483-495}
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Linking options:
https://www.mathnet.ru/eng/jsfu772
https://www.mathnet.ru/eng/jsfu/v12/i4/p483
This publication is cited in the following 1 articles:
V. K. Andreev, E. P. Magdenko, “on the Asymptotic Behavior of the Conjugate Problem Describing a Creeping Axisymmetric Thermocapillary Motion”, J. Sib. Fed. Univ.-Math. Phys., 13:1 (2020), 26–36
Citation in format AMSBIB
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