Geodesic
A priori estimates of the conjugate problem describing an axisymmetric thermocapillary motion for small Marangoni number
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 4, pp. 483-495.

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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, Marangoni number.
Mots-clés : interface 
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Victor K. Andreev; Evgeniy P. Magdenko. A priori estimates of the conjugate problem describing an axisymmetric thermocapillary motion for small Marangoni number. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 4, pp. 483-495. http://geodesic.mathdoc.fr/item/JSFU_2019_12_4_a10/

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