Geodesic
On well-posedness of inhomogeneous boundary value problem for equations of mixtures of compressible viscous fluids
Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 3, pp. 26-39.

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

The inhomogeneous boundary value problem for equations of mixture of compressible viscous fluids which is steady flow around an obstacle model are considered. Problem formulation makes it possible to vary by shape of obstacles. Well-posedness of such problem for class of strong solutions is proved. The results established in the paper can be used to make an analysis of an optimal shape for obstacles in compressible flow of mixture of viscous fluids.
Keywords: boundary value problem, mixture of viscous compressible fluids, strong solution, flow around an obstacle. 
@article{SJIM_2015_18_3_a2,
     author = {A. A. Zhalnina and N. A. Kucher},
     title = {On well-posedness of inhomogeneous boundary value problem for equations of mixtures of compressible viscous fluids},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {26--39},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2015_18_3_a2/}
}
TY  - JOUR
AU  - A. A. Zhalnina
AU  - N. A. Kucher
TI  - On well-posedness of inhomogeneous boundary value problem for equations of mixtures of compressible viscous fluids
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2015
SP  - 26
EP  - 39
VL  - 18
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2015_18_3_a2/
LA  - ru
ID  - SJIM_2015_18_3_a2
ER  - 
%0 Journal Article
%A A. A. Zhalnina
%A N. A. Kucher
%T On well-posedness of inhomogeneous boundary value problem for equations of mixtures of compressible viscous fluids
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2015
%P 26-39
%V 18
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2015_18_3_a2/
%G ru
%F SJIM_2015_18_3_a2
A. A. Zhalnina; N. A. Kucher. On well-posedness of inhomogeneous boundary value problem for equations of mixtures of compressible viscous fluids. Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 3, pp. 26-39. http://geodesic.mathdoc.fr/item/SJIM_2015_18_3_a2/

[1] Novo S., “Compressible Navier-Stokes model with inflow-outflow boundary conditions”, J. Math. Fluid Mech., 7 (2005), 485–514 | DOI | MR | Zbl

[2] Girinon V., “Navier–Stokes equations with nonhomogeneous boundary conditions in a bounded three-dimensional domain”, J. Math. Fluid Mech., 13 (2011), 309–339 | DOI | MR | Zbl

[3] Farwig R., “Stationary solutions of compressible Navier–Stokes equations with slip boundary condition”, Comm. Partial Differential Equations, 14 (1989), 1579–1606 | DOI | MR | Zbl

[4] Kweon J. R., Kellogg R. B., “Compressible Navier–Stokes equations in a bounded domain with inflow boundary condition”, SIAM J. Math. Anal., 28 (1997), 94–108 | DOI | MR | Zbl

[5] Kweon J. R., Kellogg R. B., “Regularity of solutions to the Navier–Stokes equations for compressible barotropic flows on a polygon”, Arch. Rational Mech. Anal., 163 (2000), 35–64 | DOI | MR

[6] Plotnikov P. I., Sokolovski Zh., “Statsionarnye kraevye zadachi dlya uravnenii Nave–Stoksa s pokazatelem adiabaty $\gamma3/2$”, Dokl. RAN, 397:2 (2004), 166–169 | MR

[7] Plotnikov P. I., Sokolowski J., “On compactness, domain dependence and existence of steady state solutions to compressible isothermal Navier–Stokes equations”, J. Math. Fluid Mech., 7 (2005), 529–573 | DOI | MR | Zbl

[8] Plotnikov P. I., Sokolowski J., “Domain dependence of solutions to compressible Navier–Stokes equations”, SIAM J. Control Optim., 45 (2006), 1165–1197 | DOI | MR | Zbl

[9] Plotnikov P., Sokolowski J., Compressible Navier-Stokes Equations: Theory and Shape Optimization, Springer, Basel, 2012 | MR | Zbl

[10] Rajagopal K. R., Tao L., Mechanics of Mixtures, World Sci., Singapore, 1995 | MR | Zbl

[11] Kraiko A. N., Nigmatulin R. I., “Mekhanika mnogofaznykh sred”, Itogi nauki i tekhniki. Ser. Gidromekhanika, 6, 1972, 93–174

[12] Nigmatulin R. I., Dinamika mnogofaznykh sred, Ch. 1, Nauka, M., 1987

[13] Sobolev S. L., Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Nauka, M., 1988 | MR

[14] Galdi G., An Introduction to the Mathematical Theory of the Navier–Stokes Equations: Steady-State Problems, Springer Monographs in Mathematics, Springer Sci., N.Y., 2011 | DOI | MR | Zbl