Geodesic
Existence of Weak Solutions to the First Boundary Value Problem for Equations of Mixtures of Compressible Viscous Fluids
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 3, pp. 33-53 Cet article a éte moissonné depuis la source Math-Net.Ru

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The purpose of this work is to explore a first boundary value problem for equations of mixtures of compressible viscous fluids in the steady three-dimensional case. 
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N. A. Kucher; D. A. Prokudin. Existence of Weak Solutions to the First Boundary Value Problem for Equations of Mixtures of Compressible Viscous Fluids. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 3, pp. 33-53. http://geodesic.mathdoc.fr/item/VNGU_2009_9_3_a2/

[1] Rajagopal K. R., Tao L., Mechanics of Mixtures, World Scientific, London, 1995 | MR

[2] Haupt P., Continuum Mechanics and Theory of Materials, Springer-Verlag, Berlin, 2000 | MR

[3] 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

[4] Frehse J., Goj S., Malek J., “A Uniqueness Result for a Model for Mixtures in the Absence of External Forces and Interaction Momentum”, Appl. Math., 50:6 (2005), 527–541 | DOI | MR | Zbl

[5] Goj S., Analysis for Mixtures of Fluids, Dissertation, Universitat Bonn. Math. Inst., 2005 http://bib.math.uni-bonn.de/pdf2/BMS-375.pdf | Zbl

[6] Frehse J., Weigant W., On Quasi-Stationary Compressible Miscible Mixtures, Manuscript, 2004

[7] Kazhikhov A. V., Petrov A. N., “Korrektnost nachalno-kraevoi zadachi dlya modelnoi sistemy uravnenii mnogokomponentnoi smesi”, Dinamika sploshnoi sredy, 1978, no. 35, 61–73 | MR

[8] Zlotnik A. A., “Ravnomernye otsenki i stabilizatsiya reshenii sistemy uravnenii odnomernogo dvizheniya mnogokomponentnoi barotropnoi smesi”, Matematicheskie zametki, 58:2 (1995), 307–312 | MR | Zbl

[9] Feireisl E., Novotny A., Petzeltova H., “On the Existence of Globally Defined Weak Solutions to the Navier–Stokes Equations”, Math. Fluid Mech., 3:4 (2001), 358–392 | DOI | MR | Zbl

[10] Plotnikov P. I., Sokolovski Zh., “Statsionarnye resheniya uravnenii Nave–Stoksa dlya dvukhatomnykh gazov”, Uspekhi mat. nauk, 62:3(375) (2007), 117–148 | DOI | MR | Zbl

[11] Plotnikov P. I., Sokolowski J., “On Compactness, Domain Dependence and Existence of Steady State Solutions to Compressible Isothermal Navier–Stokes Equations”, Math. Fluid Mech., 7 (2005), 529–573 | DOI | MR | Zbl

[12] Doklady Akademii Nauk, 397 (2004), 1–6 | MR

[13] Plotnikov P. I., Sokolowski J., “Concentrations of Solutions to Time-Discretized Compressible Navier–Stokes Equations”, Comm. Math. Phys., 258 (2005), 567–608 | DOI | MR | Zbl

[14] Bogovskii M. E., “O reshenii nekotorykh zadach vektornogo analiza, svyazannykh s operatorami $\mathrm{div}$ i $\mathrm{grad}$”, Trudy seminara S. L. Soboleva, 1, In-t matematiki SO AN SSSR, Novosibirsk, 1980, 5–40 | Zbl

[15] Lions P.-L., Mathematical Topics in Fluid Mechanics, v. 1, Incompressible Models, Oxford University Press, N.Y., 1996 | MR | Zbl

[16] Lions P.-L., Mathematical Topics in Fluid Mechanics, v. 2, Compressible Models, Oxford University Press, N.Y., 1998 | MR

[17] Solonnikov V. A., “Ob obschikh kraevykh zadachakh dlya sistem ellipticheskikh uravnenii v smysle A. Duglisa–L. Nirenberga, II”, Tr. matematicheskogo in-ta im. V. A. Steklova, XCII, 1966, 233–297 | Zbl

[18] Sobolev S. L., Izbrannye voprosy teorii funktsionalnykh prostranstv i obobschennykh funktsii, Nauka, M., 1989 | MR

[19] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969 | MR