Advertisement

Siberian Mathematical Journal

, Volume 33, Issue 5, pp 798–815 | Cite as

On equations for one-dimensional motion of a viscous barotropic gas in the presence of a body force

  • A. A. Zlotnik
Article

Keywords

Body Force 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ya. I. Kanel', “On a model system of equations for one-dimensional gas motion,” Differentsial'nye Uravneniya,4, No. 4, 721–734 (1968).Google Scholar
  2. 2.
    A. V. Kazhikhov, “The correctness ‘in the large’ of mixed boundary problems for the model system of equations for a viscous gas,” Dinamika Sploshn. Sredy, No. 21, 18–47 (1976).Google Scholar
  3. 3.
    A. V. Kazhikhov and V. B. Nikolaev, “On the theory of the Navier—Stokes equations for a viscous gas with a nonmonotonic state function,” Dokl. Akad. Nauk SSSR,246, No. 5, 1045–1047 (1979).Google Scholar
  4. 4.
    V. B. Nikolaev, “A boundary problem for the equations for one-dimensional barotropic motion of a viscous gas with a nonmonotonic state function,” Dinamika Sploshn. Sredy, No. 59, 130–139 (1983).Google Scholar
  5. 5.
    V. V. Shelukhin, “On the structure of the generalized solutions to one-dimensional equations for a polytropic viscous gas,” Prikl. Mat. Mech.,48, No. 6, 912–920 (1984).Google Scholar
  6. 6.
    A. A. Zlotnik and A. A. Amosov, “The generalized solutions ‘in the large’ to the equations for one-dimensional motion of a viscous barotropic gas,” Dokl. Akad. Nauk SSSR,299, No. 6, 1303–1307 (1988).Google Scholar
  7. 7.
    A. V. Kazhikhov, “On stabilization of the solutions to the initial boundary problem for the equations for a barotropic viscous fluid,” Differentsial'nye Uravneniya,15, No. 4, 662–667 (1979).Google Scholar
  8. 8.
    V. V. Shelukhin, “Periodical flows of a viscous gas,” Dinamika Sploshn. Sredy, No. 42, 80–192 (1979).Google Scholar
  9. 9.
    V. V. Shelukhin, “Bounded quasiperiodical solutions to the equations for a viscous gas,” Dinamika Sploshn. Sredy, No. 44, 147–163 (1980).Google Scholar
  10. 10.
    V. V. Shelukhin, “Propagation of initial perturbations in a viscous gas,” Sibirsk. Mat. Zh.,28, No. 2, 211–216 (1987).Google Scholar
  11. 11.
    I. Straškraba and A. Valli, “Asymptotic behavior of the density for one-dimensional Navier-Stokes equations,” Manuscripta Math.,62, No. 4, 401–416 (1988).Google Scholar
  12. 12.
    H. Beirão da Veiga, “AnL-theory for then-dimensional, stationary, compressible Navier-Stokes equations, and the incompressible limit for compressible fluids. The equilibrium solutions,” Comm. Math. Phys.,109, No. 2, 229–248 (1987).Google Scholar
  13. 13.
    A. A. Amosov and A. A. Zlotnik, “Difference schemes, correct to the second order, for equations for one-dimensional motion of a viscous gas,” Zh. Vychisl. Mat. i Mat. Fiz.,27, No. 7, 1032–1049 (1987).Google Scholar
  14. 14.
    S. N. Antontsev, A. V. Kazhikhov, and V. N. Monakhov, Boundary Problems for Mechanics of Nonhomogeneous Liquids [in Russian], Nauka, Novosibirsk (1983).Google Scholar
  15. 15.
    A. A. Zlotnik and A. A. Amosov, “On the properties of a difference scheme for the equations of one-dimensional magnetic gas dynamics,” Dinamika Soplishn. Sredy, No. 88, 47–64 (1988).Google Scholar
  16. 16.
    A. A. Amosov and A. A. Zlotnik, “A difference scheme for the equation for motion of a viscous heat-conducting gas; its properties and estimates of the error ‘in the large’,” Dokl. Akad. Nauk SSSR,284, No. 2, 265–269 (1985).Google Scholar
  17. 17.
    N. E. Keilman, “On stability of the solutions to the initial-boundary problem for equations for a barotropic gas with a viscosity depending on density,” Dinamika Sploshn. Sredy, No. 79, 36–44 (1987).Google Scholar
  18. 18.
    N. S. Nadirashvili, “On the dynamic behavior of nonlinear parabolic equations,” Dokl. Akad. Nauk SSSR,309, No. 6, 1302–1305 (1989).Google Scholar
  19. 19.
    H. Beirão da Veiga “Long time behavior for one-dimensional motion of a general barotropic fluid,” Arch. Rational Mech. Anal., 108, No. 2, 141–160 (1989).Google Scholar
  20. 20.
    H. Beirão da Veiga, “The stability of one-dimensional stationary flows of compressible viscous fluids,” Ann. Inst. H. Poincare Anal. Non Lineaire,7, No 4, 259–268 (1990).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • A. A. Zlotnik

There are no affiliations available

Personalised recommendations