Smooth solutions for the equations of compressible and incompressible fluid flow

  • Andrew Majda
Part of the Lecture Notes in Mathematics book series (LNM, volume 1047)


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  1. [1]
    BEBERNES, J., and A. BRESSAN: "Thermal behavior for a confined reactive gas", J. Differential Equations 44 (1982), 118–133.ADSMathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    CHORIN, A.J.: "The evolution of a turbulent vortex", Comm. Math. Phys. 83 (1982), 517–536.ADSMathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    COURANT, R., and D. HILBERT: Methods of Mathematical Physics, Vol. II, Wiley-Interscience, New York, 1963.MATHGoogle Scholar
  4. [4]
    CRANDALL, M., and P. SOUGANIDIS: (in preparation).Google Scholar
  5. [5]
    DOUGLIS, A.: "Some existence theorems for hyperbolic systems of partial differential equations in two independent variables", Comm. Pure Appl. Math. 5 (1952), 119–154.MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    EBIN, D.: "The motion of slightly compressible fluids viewed as motion with a strong constraining force", Ann. Math. 150 (1977), 102–163.MathSciNetMATHGoogle Scholar
  7. [7]
    EBIN, D.: "Motion of slightly compressible fluids in a bounded domain. I", Comm. Pure Appl. Math. 35 (1982), 451–487.MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    EMBID, P., and A. Majda: "Slightly compressible combustible fluds" (in preparation).Google Scholar
  9. [9]
    GEYMONAT, G., and E. SANCHEZ-PALEWCIA: "On the vanishing viscosity limit for acoustic phenomena in a bounded region", Arch. Rational Mech. Anal. 75 (1981), 257–268.ADSMathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    HARTMAN, P., and A. WINTER: "On hyperbolic differential equations", Amer. J. Math. 74 (1952), 834–864.MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    KASSOY, D. R., and J. POLAND: "The thermal explosion confined by a constant temperature boundary: II-the extremely rapid transient", SIAM J. Appl. Math. 41 (1981), 231–246.MathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    KASSOY, D. R., and J. BEBERNES: "Gasdynamic aspects of thermal explosions", Trans. of Twenty-Seventh Conference of Army Math., pp. 687–706.Google Scholar
  13. [13]
    KATO, T.: "Quasi-linear equations of evolution with applications to partial differential equations", Lecture Notes in Math. 448, Springer-Verlag (1975), 25–70.MathSciNetCrossRefGoogle Scholar
  14. [14]
    KATO, T.: "The Cauchy problem for quasi-linear symmetric hyperbolic systems", Arch. Rational Mech. Anal. 58 (1975), 181–205.ADSMathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    KLAINERMAN, S., and A. MAJDA: "Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids", Comm. Pure Appl. Math. 34 (1981), 481–524.ADSMathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    KLAINERMAN, S., and A. MAJDA: "Compressible and incompressible fluids", Comm. Pure Appl. Math. 35 (1982), 629–653.ADSMathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    KLAINERMAN, S., and R. KOHN: "Compressible and incompressible elasticity" (in preparation).Google Scholar
  18. [18]
    KREISS, H. O.: "Problems with different time scales for partial differential equations", Comm. Pure Appl. Math. 33 (1980), 399–441.MathSciNetCrossRefMATHGoogle Scholar
  19. [19]
    LAX, P. D.: "Hyperbolic systems of conservation laws and the mathematical theory of shock waves", SIAM Reg. Conf. Lecture #11, Philadelphia, 1973.Google Scholar
  20. [20]
    LIONS, J. L.: Quelques Methodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod, Paris, 1969.MATHGoogle Scholar
  21. [21]
    MAJDA, A.: "Equations for low Mach number combustion", (to appear in Comb. Sci. and Tech.).Google Scholar
  22. [22]
    MATKOWSKY, B. J., and G. I. SIVASHINSKY: "An asymptotic derivation of two models in flame theory associated with the constant density approximation", SIAM J. Appl. Math. 37 (1979), 686–699.MathSciNetCrossRefMATHGoogle Scholar
  23. [23]
    MATSUMURA, A., and T. NISHIDA: "The initial value problem for the equations of motion of various and heat-conductive gases", J. Math. Kyoto Univ. 20 (1980), 67–104.MathSciNetCrossRefMATHGoogle Scholar
  24. [24]
    MOSER, J.: "A rapidly convergent iteration method and nonlinear differential equations", Ann. Scuola Norm. Sup. Pisa 20 (1966), 265–315.MathSciNetMATHGoogle Scholar
  25. [25]
    TEMAM, R.: "Local existence of C solutions of the Euler equations of incompressible perfect fluids", in Turbulence and the Navier-Stokes Equations, Springer-Verlag, New York, 1976, 184–194.CrossRefGoogle Scholar
  26. [26]
    TEMAM, R.: The Navier-Stokes Equations, North Holland, Amsterdam, 1977.MATHGoogle Scholar
  27. [27]
    BEIRAO DA VEIGA, H.: "On the solutions in the large of the two-diemnsional flow of a non-viscous incompressible fluid" (preprint).Google Scholar
  28. [28]
    CHORIN, A. J.: "A numerical method for solving incompressible viscous flow problems", J. Comput. Phys. 2 (1967), 12–26.ADSCrossRefMATHGoogle Scholar
  29. [29]
    GHONIEM, A.F., A.J. CHORIN, and A. K. OPPENHEIM: "Numerical modelling of turbulent flow in a combustion tunnel", Philos. Trans. Roy. Soc. London Ser. A (1981), 1103–1119.Google Scholar
  30. [30]
    HALTINER, G. J. and R. T. WILLIAMS: Numerical Weather Prediction and Dynomic Meteorology, 2nd Edition, Wiley, New York, 1980.Google Scholar
  31. [31]
    MAJDA, A.: "The existence of multi-dimensional shock fronts", Memoirs Amer. Math. Soc. (to appear 1983).Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Andrew Majda
    • 1
  1. 1.University of California, BerkeleyBerkeleyUSA

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