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Literature cited
L. I. Sedov, Mechanics of the Continuous Medium [in Russian], Vol. 2, Nauka, Moscow (1970).
Ya. I. Voitkunskii, V. B. Amfilokhiev, and V. A. Pavlovskii, “The motion equations of a fluid taking into account its relaxational properties,” Tr. Leningr. Korablestroit. Inst., No. 69 (1970).
V. A. Pavlovskii, “On the question of the theoretical description of weak aqueous solutions of polymers,” Dokl. Akad. Nauk SSSR,200, No. 4 (1971).
J. Serrin, Mathematical Foundation of Classical Fluid Mechanics [Russian translation], IIL, Moscow (1963).
O. A. Ladyzhenskaya, Mathematical Problems of the Dynamics of a Viscous Incompressible Fluid [in Russian], Nauka, Moscow (1970).
A. P. Oskolkov, “On the solvability in the large of the first boundary-value problem for a third-order quasilinear system encountered in the investigation of the motion of a viscous fluid,” Zap. Nauchn. Sem. LOMI,27, 145–160 (1972).
O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York (1968).
A. P. Oskolkov, “On the uniqueness and global solvability of the first boundary-value problem for a system of equations describing the motion of aqueous solutions of polymers,” Tr. Leningr. Korablestr. Inst., No. 80 (1972).
A. P. Oskolkov, “On a quasilinear parabolic system with a small parameter, approximating the Navier-Stokes system of equations,” Zap. Nauchn. Sem. LOMI,21, 79–103 (1971).
K. K. Golovkin and A. Krzywicki, “On the regularity with respect to time of weak solutions of the Navier-Stokes equations,” Coll. Math.,16, 163–172 (1967).
I. I. Varlamkina and A. P. Oskolkov, “On a nonstationary quasilinear system, describing the slow motion of water solutions of polymers and regularizing the system of Navie-Stokes equations,” Tr. Leningr. Korablestr. Inst. (in print).
L. D. Landau and E. M. Lifshits, Mechanics of Continuous Media [in Russian], Gostekhizdat, Moscow (1953).
U. L. Uilkinson, Non-Newtonian Fluids [Russian translation], Mir, Moscow (1964).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 38, pp. 98–136, 1973.
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Oskolkov, A.P. The uniqueness and global solvability of boundary-value problems for the equations of motion for aqueous solutions of polymers. J Math Sci 8, 427–455 (1977). https://doi.org/10.1007/BF01084613
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DOI: https://doi.org/10.1007/BF01084613