Geodesic
On a mathematical model of non-isothermal creeping flows of a fluid through a given domain
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 23 (2019) no. 3, pp. 417-429

Voir la notice de l'article provenant de la source Math-Net.Ru

We study a mathematical model describing steady creeping flows of a non-uniformly heated incompressible fluid through a bounded 3D domain with locally Lipschitz boundary. The model under consideration is a system of second-order nonlinear partial differential equations with mixed boundary conditions. On in-flow and out-flow parts of the boundary the pressure, the temperature and the tangential component of the velocity field are prescribed, while on impermeable solid walls the no-slip condition and a Robin-type condition for the temperature are used. For this boundary-value problem, we introduce the concept of a weak solution (a pair “velocity–temperature”), which is defined as a solution to some system of integral equations. The main result of the work is a theorem on the existence of weak solutions in a subspace of the Cartesian product of two Sobolev's spaces. To prove this theorem, we give an operator interpretation of the boundary value problem, derive a priori estimates of solutions, and apply the Leray–Schauder fixed point theorem. Moreover, energy equalities are established for weak solutions.
Mots-clés : flux problem
Keywords: non-isothermal flows, creeping flows, mixed boundary conditions, weak solutions. 
@article{VSGTU_2019_23_3_a1,
     author = {A. A. Domnich and E. S. Baranovskii and M. A. Artemov},
     title = {On a mathematical model of non-isothermal creeping flows of a fluid through a given domain},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {417--429},
     publisher = {mathdoc},
     volume = {23},
     number = {3},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2019_23_3_a1/}
}
TY  - JOUR
AU  - A. A. Domnich
AU  - E. S. Baranovskii
AU  - M. A. Artemov
TI  - On a mathematical model of non-isothermal creeping flows of a fluid through a given domain
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2019
SP  - 417
EP  - 429
VL  - 23
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2019_23_3_a1/
LA  - ru
ID  - VSGTU_2019_23_3_a1
ER  - 
%0 Journal Article
%A A. A. Domnich
%A E. S. Baranovskii
%A M. A. Artemov
%T On a mathematical model of non-isothermal creeping flows of a fluid through a given domain
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2019
%P 417-429
%V 23
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2019_23_3_a1/
%G ru
%F VSGTU_2019_23_3_a1
A. A. Domnich; E. S. Baranovskii; M. A. Artemov. On a mathematical model of non-isothermal creeping flows of a fluid through a given domain. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 23 (2019) no. 3, pp. 417-429. http://geodesic.mathdoc.fr/item/VSGTU_2019_23_3_a1/