Advertisement

Irreducible Chapman–Enskog Projections and Navier–Stokes Approximations

  • Evgenii Radkevich
Part of the International Mathematical Series book series (IMAT, volume 7)

Keywords

Cauchy Problem Quantization System Matrix Equation Invariant Manifold Moment Approximation 
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.
    A. V. Babin and M. I. Vishik, Attractors of Evolution Equations, North- Holland, Amsterdam etc., 1992.Google Scholar
  2. 2.
    A. V. Bobylev, Chapman–Enskog adn Grad methods for solving the Boltzmann equation[in Russian], Dokl. Akad. Nauk SSSR 27(1982), no. 1, 29-33.MathSciNetGoogle Scholar
  3. 3.
    S. C. Chapman and Cowling T. C., The Mathematical Theory of Non- Uniform Gases, Cambridge Univ. Press, Cambridge, 1970.Google Scholar
  4. 4.
    G. Q. Chen, C. D. Levermore, and T.-P. Lui, Hyperbolic conservation laws with stiff relaxation terms and entropy, Commun. Pure Appl. Math. 47(1994), no. 6, 787-830.MATHCrossRefGoogle Scholar
  5. 5.
    W. Dreyer and H. Struchtrup, Heat pulse experiments revisted, Contin. Mech. Thermodyn. 5(1993), 3-50.CrossRefMathSciNetGoogle Scholar
  6. 6.
    A. V. Fursikov, Stabilizability of a quasi-linear parabolic equation by means of a boundary control with feedback, Sb. Math. 192(2001), no.4, 593-639.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    S. I. Gelfand, On the number of solutions to the quadratic equations[in Russian], In: Globus, Moscow, 2004, pp. 124-133.Google Scholar
  8. 8.
    S. K. Godunov, An interesting class of quasilinear systems, Sov. Math. Dokl. 2(1961), 947-949.MATHGoogle Scholar
  9. 9.
    A. N. Gorban and I. V. Karlin, Invariant Manifolds for Physical and Chemical Kinetic, Springer-Verlag, 2005.Google Scholar
  10. 10.
    A. Yu. Goritskii, Construction of attracting integral manifolds of a dissipative hyperbolic equation. [To appear]Google Scholar
  11. 11.
    V. V. Kozlov, Restrictions of quadratic forms to Lagrangian planes, quadratic matrix equations, and gyroscopic stabilization, Funct. Anal. Appl. 39(2005), no. 4, 271-283.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    J. C. Maxwell, A Treatise on Electricity and Magnetism, Dover Publ., New York, 1954.MATHGoogle Scholar
  13. 13.
    I. M¨uller and T. Ruggeri, Extended Thermodynamics, Springer-Verlag, 1993.Google Scholar
  14. 14.
    V. V. Palin, On the solvability of matrix equations[in Russian], Vestnik Mosk. Gos. Univ. [To appear]Google Scholar
  15. 15.
    V. V. Palin and E. V. Radkevich, Navier–Stokes approximation and problem of the Chapman-Enskog projection for kinetic equation, J. Math. Sci., New York 135(2006), no. 1, 2721-2748.MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    R. Peierls, Zur kinetischen throrie der warmeleitung in kristallen, Ann. Phys. 3(1929), 1055.Google Scholar
  17. 17.
    E. V. Radkevich, Chapman–Enskog projections and problems of Navier– Stokes Approximations, Tr. Steklov Mat. Inst. 250(2005), 219-225.MathSciNetGoogle Scholar
  18. 18.
    E. V. Radkevich, Mathematical Aspects of Nonequillibrium Processes[in Russian], “Tamara Rozhkovskaya”’, Novosibirsk, 2007.Google Scholar
  19. 19.
    T. S. Sideris, B. Tomases, and D.Wang, Long time behavior of solutions to the 3D compressible Euler equations with damping, Commun. Partial Differ. Equations 28(2003), no.3-4, 795-816.MATHCrossRefGoogle Scholar
  20. 20.
    L. Tongxing, Solution of the matrix equation AX -XB= C, Computing 37(1986), 351-355.Google Scholar
  21. 21.
    W. Wang and T. Yang, The pointwise estimates of solution for Euler equations with damping in multi-dimensionsJ. Differ. Equations 173(2001), no. 2, 410-450MATHCrossRefGoogle Scholar
  22. 22.
    L. R. Volevich and E. V. Radkevich, the Cauchy problem for hyperbolic equations with small parameter at the higher order derivatives, Trudy Mosk. Mat. o-va 65(2004), 69-113.MathSciNetGoogle Scholar
  23. 23.
    L. R. Volevich and E. V. Radkevich, Uniform estimates of solutions of the Cauchy problem for hyperbolic equations with a small parameter multiplying higher derivatives, Differ. Equ. 39(2003), no. 4, 521-535.MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    I. Zagrebaev and E. Radkevich, On the problems of the Navier–Stokes approximation to the mixed problem for the Biot system of equations. [To appear]Google Scholar
  25. 25.
    N. A. Zhura and A. N. Oraevskii, The Cauchy problem for one hyperbolic system with constant coe.cientsDokl. Math. 69(2004), no. 3, 419-422.MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Evgenii Radkevich
    • 1
  1. 1.Moscow State UniversityRussia

Personalised recommendations