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Mat. Zametki, 2018, Volume 103, Issue 1, Pages 147–157 (Mi mz11426)  

A Priori Estimates of the Solution of the Problem of the Unidirectional Thermogravitational Motion of a Viscous Liquid in the Plane Channel

E. N. Cheremnykhab

a Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences, Krasnoyarsk
b Siberian Federal University, Krasnoyarsk

Abstract: We consider an initial boundary-value problem describing the unidirectional motion of a liquid in the Oberbeck–Boussinesq model in a plane channel with rigid immovable walls on which the temperature distribution is given (or the upper wall is heat-insulated). For this problem, we obtain a priori estimates, find an exact stationary solution, and determine conditions under which the solution converges to its stationary regime.

Keywords: initial boundary-value problem, inverse problem, a priori estimate.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00067


DOI: https://doi.org/10.4213/mzm11426

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English version:
Mathematical Notes, 2018, 103:1, 145–154

Bibliographic databases:

UDC: 517
Received: 25.10.2016
Revised: 28.04.2017

Citation: E. N. Cheremnykh, “A Priori Estimates of the Solution of the Problem of the Unidirectional Thermogravitational Motion of a Viscous Liquid in the Plane Channel”, Mat. Zametki, 103:1 (2018), 147–157; Math. Notes, 103:1 (2018), 145–154

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm11426
  • http://mi.mathnet.ru/eng/mz/v103/i1/p147

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