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, 2018, Volume 103, Issue 1,Pages <nobr>147

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

E. N. Cheremnykh^ab

^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.

UDC: 517

Received: 25.10.2016
Revised: 28.04.2017

DOI: 10.4213/mzm11426