Solvability of a regularized boundary-value problem for the system of equations of dynamics of mixtures of viscous compressible heat-conducting fluids
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 300-312 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider the boundary–value problem for the system of nonlinear partial differential equations which arise in the analysis of stationary motions of mixtures of viscous compressible heat–conducting fluids in a bounded domain of three–dimensional space. We prove the existence of strong solutions to the regularized boundary value problem.
Keywords: existence theorem, stationary boundary value problem, viscous compressible heat–conducting fluid, multi–velocity mixture.
@article{SEMR_2020_17_a84,
     author = {D. A. Prokudin},
     title = {Solvability of a regularized boundary-value problem for the system of equations of dynamics of mixtures of viscous compressible heat-conducting fluids},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {300--312},
     year = {2020},
     volume = {17},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a84/}
}
TY  - JOUR
AU  - D. A. Prokudin
TI  - Solvability of a regularized boundary-value problem for the system of equations of dynamics of mixtures of viscous compressible heat-conducting fluids
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2020
SP  - 300
EP  - 312
VL  - 17
UR  - http://geodesic.mathdoc.fr/item/SEMR_2020_17_a84/
LA  - en
ID  - SEMR_2020_17_a84
ER  - 
%0 Journal Article
%A D. A. Prokudin
%T Solvability of a regularized boundary-value problem for the system of equations of dynamics of mixtures of viscous compressible heat-conducting fluids
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2020
%P 300-312
%V 17
%U http://geodesic.mathdoc.fr/item/SEMR_2020_17_a84/
%G en
%F SEMR_2020_17_a84
D. A. Prokudin. Solvability of a regularized boundary-value problem for the system of equations of dynamics of mixtures of viscous compressible heat-conducting fluids. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 300-312. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a84/

[1] E. Feireisl, Dynamics of viscous compressible fluids, Oxford University Press, Oxford, 2004 | MR | Zbl

[2] E. Feireisl, A. Novotny, Singular limits in thermodynamics of viscous fluids, Birkhauser, Basel, 2009 | MR | Zbl

[3] P.B. Mucha, M. Pokorny, “On the steady compressible Navier–Stokes–Fourier system”, Comm. Math. Phys, 288:1 (2009), 349–377 | MR | Zbl

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

[5] A.E. Mamontov, D.A. Prokudin, “Viscous compressible multi-fluids: modeling and multi–D existence”, Methods Appl. Anal., 20:2 (2013), 179–196 | MR | Zbl

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

[7] A. Novotny, I. Straskraba, Introduction to the mathematical theory of compressible flow, Oxford University Press, Oxford, 2004 | MR | Zbl

[8] S. Agmon, A. Douglis, L. Nirenberg, “Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I”, Comm. Pure Appl. Math., 12:4 (1959), 623–727 | MR | Zbl

[9] S. Agmon, A. Douglis, L. Nirenberg, “Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II”, Comm. Pure Appl. Math., 17:1 (1964), 35–92 | MR | Zbl

[10] D. Gilbarg, N. S. Trudinger, Elliptic partial differential equations of second order, Springer–Verlag, Berlin, 1983 | MR | Zbl

[11] M.E. Bogovskii, “The solution of some problems of vector analysis related to the operators ${\rm div}$ and ${\rm grad}$”, Trudy sem. S.L. Soboleva, 1, 1980, 5–40 | MR | Zbl