Mathematical Notes

, Volume 103, Issue 1–2, pp 145–154 | Cite as

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



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.


initial boundary-value problem inverse problem a priori estimate 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Institute of Numerical SimulationRussian Academy of SciencesKrasnoyarskRussia
  2. 2.Siberian Federal UniversityKrasnoyarskRussia

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