Geodesic
A Priori Estimates of the Solution of the Problem of the Unidirectional Thermogravitational Motion of a Viscous Liquid in the Plane Channel
Matematičeskie zametki, Tome 103 (2018) no. 1, pp. 147-157

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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. 
@article{MZM_2018_103_1_a12,
     author = {E. N. Cheremnykh},
     title = {A {Priori} {Estimates} of the {Solution} of the {Problem} of the {Unidirectional} {Thermogravitational} {Motion} of a {Viscous} {Liquid} in the {Plane} {Channel}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {147--157},
     publisher = {mathdoc},
     volume = {103},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_1_a12/}
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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. Matematičeskie zametki, Tome 103 (2018) no. 1, pp. 147-157. http://geodesic.mathdoc.fr/item/MZM_2018_103_1_a12/