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Navier-Stoke equations; method of a discretization in time; global existence of weak solutions; mixed initial-boundary value problem; viscous compressible fluid

References:

[1] O. A. Ladyzhenskaya N. N. Uralceva: **Linear and Quasilinear Equations of the Elliptic Type**. Nauka, Moscow, 1973 (Russian). MR 0509265

[2] L. G. Loicianskij: **Mechanics of Liquids and Gases**. Nauka, Moscow, 1973 (Russian).

[3] A. Matsumura T. Nishida: **The Initical Value Problem for the Equations of Motion of Viscous and Heat-Conductive Gases**. J. Math. Kyoto Univ. 20 (1980), 67-104, MR 0564670

[4] J. Neustupa: **A Note to the Global Weak Solvability of the Navier-Stokes Equations for Compressible Fluid**. to appear prob. in Apl. mat. MR 0961316

[5] R. Rautmann: **The Uniqueness and Regularity of the Solutions of Navier-Stokes Problems**. Functional Theoretic Methods for Partial Differential Equations, Proc. conf. Darmstadt 1976, Lecture Notes in Mathematics, Vol. 561, Berlin-Heidelberg-New York, Springer-Verlag, 1976, 378-393. MR 0463727 | Zbl 0383.35059

[6] V. A. Sollonikov: **The Solvability of an Initial-Boundary Value Problem for the Equations of Motion of Viscous Compressible Fluid**. J. Soviet Math. 14 (1980), 1120-1133 (previously in Zap. Nauchn. Sem. LOMI 56 (1976), 128-142 (Russian)). DOI 10.1007/BF01562053 | MR 0481666

[7] R. Temam: **Navier-Stokes Equations**. North-Holland Publishing Company, Amsterdam- New York-Oxford, 1977. MR 0769654 | Zbl 0383.35057

[8] A. Valli: **An Existence Theorem for Compressible Viscous Fluids**. Ann. Mat. Рurа Appl. 130 (1982), 197-213. DOI 10.1007/BF01761495 | MR 0663971 | Zbl 0599.76082

[9] A. Valli: **Periodic and Stationary Solutions for Compressible Navier-Stokes Equations via a Stability Method**. Ann. Scuola Norm. Sup. Pisa, (IV) 10 (1983), 607-647. MR 0753158 | Zbl 0542.35062