Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2006, Article ID 12497, 27 pages
http://dx.doi.org/10.1155/AAA/2006/12497

Research of a mathematical model of low-concentrated aqueous polymer solutions

Voronezh State University, Universitetskaya pl.1, Voronezh 394 006, Russia

Received 12 March 2005; Accepted 10 July 2005

Copyright © 2006 Mikhail V. Turbin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. V. B. Amfilohiev and V. A. Pavlovsky, “Experimental data about laminar-turbulent passage at flow of a polymer solutions in pipes,” Trudy Leningradskogo korablestroitelnogo Instituta, vol. 104, pp. 3–5, 1976 (Russian). View at Google Scholar
  2. V. B. Amfilohiev, Ya. I. Vojtkunsky, N. P. Mazaeva, and Ya. S. Khodorkovsky, “The flow of a polymer solutions at presence of convective accelerations,” Trudy Leningradskogo korablestroitelnogo Instituta, vol. 96, pp. 3–9, 1975 (Russian). View at Google Scholar
  3. A. M. Freudental and H. Geiringer, “The mathematical theories of the inelastic continuum,” in Handbuch der Physik, herausgegeben von S. Flügge. Bd. 6. Elastizität und Plastizität, pp. 229–433, Springer, Berlin, 1958. View at Google Scholar · View at MathSciNet
  4. H. Gajewski, K. Gröger, and K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, vol. 38 of Mathematische Lehrbücher und Monographien, II. Abteilung, Mathematische Monographien, Akademie, Berlin, 1974. View at Zentralblatt MATH · View at MathSciNet
  5. O. A. Ladyzhenskaya, “On the nonstationary Navier-Stokes equations,” Vestnik Leningrad University. Mathematics, vol. 13, no. 19, pp. 9–18, 1958 (Russian). View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Fizmatgiz, Moscow, 1961.
  7. O. A. Ladyzhenskaya, “On errors in two of my publications on Navier-Stokes equations and their corrections,” Rossiĭ skaya Akademiya Nauk. Sankt-Peterburgskoe Otdelenie. Matematicheskiĭ Institut im. V. A. Steklova. Zapiski Nauchnykh Seminarov (POMI), vol. 271, pp. 151–155, 316, 2000 (Russian). View at Google Scholar · View at MathSciNet
  8. J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod; Gauthier-Villars, Paris, 1969. View at Zentralblatt MATH · View at MathSciNet
  9. V. G. Lītvīnov, Motion of a Nonlinearly Viscous Fluid, Nauka, Moscow, 1982. View at Zentralblatt MATH · View at MathSciNet
  10. N. G. Lloyd, Degree Theory, Cambridge Tracts in Mathematics, no. 73, Cambridge University Press, Cambridge, 1978. View at Zentralblatt MATH · View at MathSciNet
  11. A. P. Oskolkov, “Solvability in the large of the first boundary value problem for a certain quasilinear third order system that is encountered in the study of the motion of a viscous fluid,” Zapiski Naučnyh Seminarov Leningradskogo Otdelenija Matematičeskogo Instituta im. V. A. Steklova Akademii Nauk SSSR (LOMI), vol. 27, pp. 145–160, 1972 (Russian). View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. A. P. Oskolkov, “The uniqueness and solvability in the large of boundary value problems for the equations of motion of aqueous solutions of polymers,” Zapiski Naučnyh Seminarov Leningradskogo Otdelenija Matematičeskogo Instituta im. V. A. Steklova Akademii Nauk SSSR (LOMI), vol. 38, pp. 98–136, 1973 (Russian). View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. A. P. Oskolkov, “Some quasilinear systems that arise in the study of the motion of viscous fluids,” Zapiski Naučnyh Seminarov Leningradskogo Otdelenija Matematičeskogo Instituta im. V. A. Steklova Akademii Nauk SSSR (LOMI), vol. 52, pp. 128–157, 219, 1975. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. A. P. Oskolkov, “Some nonstationary linear and quasilinear systems that arise in the study of the motion of viscous fluids,” Zapiski Naučnyh Seminarov Leningradskogo Otdelenija Matematičeskogo Instituta im. V. A. Steklova Akademii Nauk SSSR (LOMI), vol. 59, pp. 133–177, 257, 1976 (Russian). View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. A. P. Oskolkov, “Initial-boundary value problems with a sliding boundary condition for modified Navier-Stokes equations,” Rossiĭ skaya Akademiya Nauk. Sankt-Peterburgskoe Otdelenie. Matematicheskiĭ Institut im. V. A. Steklova. Zapiski Nauchnykh Seminarov (POMI), vol. 213, pp. 93–115, 225–226, 1994 (Russian). View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. V. A. Pavlovsky, “To a problem on theoretical exposition of weak aqueous solutions of polymers,” Doklady Akademii Nauk SSSR, vol. 200, no. 4, pp. 809–812, 1971 (Russian). View at Google Scholar
  17. R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis, AMS Chelsea, Rhode Island, 2001.
  18. Ya. I. Vojtkunsky, V. B. Amfilohiev, and V. A. Pavlovsky, “Equations of motion of a liquid with taking into account its relaxational properties,” Trudy Leningradskogo korablestroitelnogo Instituta, vol. 69, pp. 19–26, 1970 (Russian). View at Google Scholar
  19. V. G. Zvyagin and V. T. Dmitrienko, The Approximating Approach to Research of Problems of Fluid Dynamics. The Navier-Stokes System, Editorial URSS, Moscow, 2004.