Geodesic
Existence of solutions of the boundary value problem for the equations of barotropic flows of a multicomponent medium. I. Statement of the main problem. Solvability of an auxiliary problem
Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 4, pp. 77-92.

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

The problem of steady barotropic motion of a multicomponent medium consisting of viscous compressible fluids in a bounded domain of three-dimensional space is formulated. The viscosity matrices are assumed to be arbitrary (nondiagonal). The solvability of a regularized (approximate) problem is proved.
Keywords: existence theorem, steady barotropic flow, viscosity matrix.
Mots-clés : viscous compressible multifluid 
@article{SJIM_2023_26_4_a5,
     author = {A. E. Mamontov and D. A. Prokudin},
     title = {Existence of solutions of the boundary value problem for the equations of barotropic flows of a multicomponent medium. {I.} {Statement} of the main problem. {Solvability} of an auxiliary problem},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {77--92},
     publisher = {mathdoc},
     volume = {26},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2023_26_4_a5/}
}
TY  - JOUR
AU  - A. E. Mamontov
AU  - D. A. Prokudin
TI  - Existence of solutions of the boundary value problem for the equations of barotropic flows of a multicomponent medium. I. Statement of the main problem. Solvability of an auxiliary problem
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2023
SP  - 77
EP  - 92
VL  - 26
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2023_26_4_a5/
LA  - ru
ID  - SJIM_2023_26_4_a5
ER  - 
%0 Journal Article
%A A. E. Mamontov
%A D. A. Prokudin
%T Existence of solutions of the boundary value problem for the equations of barotropic flows of a multicomponent medium. I. Statement of the main problem. Solvability of an auxiliary problem
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2023
%P 77-92
%V 26
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2023_26_4_a5/
%G ru
%F SJIM_2023_26_4_a5
A. E. Mamontov; D. A. Prokudin. Existence of solutions of the boundary value problem for the equations of barotropic flows of a multicomponent medium. I. Statement of the main problem. Solvability of an auxiliary problem. Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 4, pp. 77-92. http://geodesic.mathdoc.fr/item/SJIM_2023_26_4_a5/

[1] Rajagopal K. L., Tao L., Mechanics of mixtures, World Scientific, N. J., 1995 | MR | Zbl

[2] R. I. Nigmatulin, Dynamics of Multiphase Media, v. 1, Nauka, M., 1987 (in Russian)

[3] Mamontov A. E., Prokudin D. A., “Viscous compressible homogeneous multi-fluids with multiple velocities: barotropic existence theory”, Siberian Electron. Math. Rep., 14 (2017), 388–397 | MR | Zbl

[4] V. N. Dorovskii and Yu. V. Perepechko, “Phenomenological description of two-velocity media with relaxing tangential stresses”, Prikl. Mekh. Tekh. Fiz., 1992, no. 3, 97–104 (in Russian)

[5] A. M. Blokhin and V. N. Dorovskii, Problems of Mathematical Modeling in the Theory of Multivelocity Continuum, OIGGM, Novosibirsk, 1994 (in Russian)

[6] Frehse J., Goj S., Malek J., “On a Stokes-like system for mixtures of fluids”, SIAM J. Math. Anal., 36:4 (2005), 1259–1281 | DOI | MR | Zbl

[7] Frehse J., Weigant W., “On quasi-stationary models of mixtures of compressible fluids”, Appl. Math., 53:4 (2008), 319–345 | DOI | MR | Zbl

[8] A. E. Mamontov and D. A. Prokudin, “Solvability of a stationary boundary value problem for equations of polytropic motion of viscous compressible multifluid media”, Sib. Elektron. Mat. Izv., 13 (2016), 664–693 (in Russian) | Zbl

[9] V. G. Maz'ya, Sobolev Spaces, Izd. Leningrad. Univ., L., 1985 (in Russian) | MR

[10] S. M. Nikol'skii, Approximation of Functions of Several Variables and Embedding Theorems, Nauka, M., 1977 (in Russian) | MR

[11] V. A. Trenogin, Functional Analysis, Fizmatlit, M., 2002 (in Russian) | MR

[12] Novotný A., Straškraba I., Introduction to the mathematical theory of compressible flow, Oxford University Press, Oxford, 2004 | MR | Zbl

[13] Mucha P., Pokorny M., “Weak solutions to equations of steady compressible heat conducting fluids”, Math. Models Methods Appl. Sci., 20:5 (2010), 785–813 | DOI | MR | Zbl

[14] O. A. Ladyzhenskaya, Boundary Value Problems of Mathematical Physics, Nauka, M., 1973 (in Russian) | MR

[15] L. A. Solonnikov, “On general boundary value problems for systems of Douglis—Nirenberg elliptic equations. II”, Trudy Mat. Inst. Steklov, 42, 1966, 233–297 (in Russian)

[16] Agmon S., Douglis A., Nirenberg L., “Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II”, Comm. Pure Appl. Math., 17 (1964), 35–92 | DOI | MR | Zbl