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This article is cited in 9 scientific papers (total in 9 papers)
A joint creeping motion of three fluids in a flat layer: a priori estimates and convergence to a stationary regime
V. K. Andreevab, E. N. Cheremnykhab a Institute of Computational Modeling SB RAS, 50/44 Akademgorodok, 660036 Krasnoyarsk
b Siberian Federal University, 79 Svobodnyi av., 660041 Krasnoyarsk
Abstract:
We study a partially invariant solution of rank 2 and defect 3e to the equations of a viscous heat-conducting fluid. It is interpreted as a two-dimensional motion of three immiscible fluids in a flat channel bounded by solid walls for which the distribution of temperature is known. From a mathematical point of view, the resulting initial boundary value problem is nonlinear and inverse. Under some assumptions (often fulfilled in practical applications), the problem is replaced by a linear one. We obtain a priori estimates as well as the exact stationary solution and prove that, the solution tends to a stationary regime if the temperatures of the walls stabilize with time.
Keywords:
thermocapillarity, a priori estimate, conjugate boundary value problem, asymptotic behavior.
Received: 16.05.2015
Citation:
V. K. Andreev, E. N. Cheremnykh, “A joint creeping motion of three fluids in a flat layer: a priori estimates and convergence to a stationary regime”, Sib. Zh. Ind. Mat., 19:1 (2016), 3–17; J. Appl. Industr. Math., 10:1 (2016), 7–20
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https://www.mathnet.ru/eng/sjim907 https://www.mathnet.ru/eng/sjim/v19/i1/p3
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Abstract page: | 346 | Full-text PDF : | 71 | References: | 84 | First page: | 56 |
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