Skip to main content

Smooth solutions for the equations of compressible and incompressible fluid flow

Part of the Lecture Notes in Mathematics book series (LNMCIME,volume 1047)

This is a preview of subscription content, access via your institution.

Buying options

eBook
USD   19.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   26.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. BEBERNES, J., and A. BRESSAN: "Thermal behavior for a confined reactive gas", J. Differential Equations 44 (1982), 118–133.

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  2. CHORIN, A.J.: "The evolution of a turbulent vortex", Comm. Math. Phys. 83 (1982), 517–536.

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  3. COURANT, R., and D. HILBERT: Methods of Mathematical Physics, Vol. II, Wiley-Interscience, New York, 1963.

    MATH  Google Scholar 

  4. CRANDALL, M., and P. SOUGANIDIS: (in preparation).

    Google Scholar 

  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. EBIN, D.: "The motion of slightly compressible fluids viewed as motion with a strong constraining force", Ann. Math. 150 (1977), 102–163.

    MathSciNet  MATH  Google Scholar 

  7. EBIN, D.: "Motion of slightly compressible fluids in a bounded domain. I", Comm. Pure Appl. Math. 35 (1982), 451–487.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. EMBID, P., and A. Majda: "Slightly compressible combustible fluds" (in preparation).

    Google Scholar 

  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.

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  10. HARTMAN, P., and A. WINTER: "On hyperbolic differential equations", Amer. J. Math. 74 (1952), 834–864.

    CrossRef  MathSciNet  MATH  Google Scholar 

  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

  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. KATO, T.: "Quasi-linear equations of evolution with applications to partial differential equations", Lecture Notes in Math. 448, Springer-Verlag (1975), 25–70.

    CrossRef  MathSciNet  Google Scholar 

  14. KATO, T.: "The Cauchy problem for quasi-linear symmetric hyperbolic systems", Arch. Rational Mech. Anal. 58 (1975), 181–205.

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  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.

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  16. KLAINERMAN, S., and A. MAJDA: "Compressible and incompressible fluids", Comm. Pure Appl. Math. 35 (1982), 629–653.

    CrossRef  ADS  MathSciNet  MATH  Google Scholar 

  17. KLAINERMAN, S., and R. KOHN: "Compressible and incompressible elasticity" (in preparation).

    Google Scholar 

  18. KREISS, H. O.: "Problems with different time scales for partial differential equations", Comm. Pure Appl. Math. 33 (1980), 399–441.

    CrossRef  MathSciNet  MATH  Google Scholar 

  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. LIONS, J. L.: Quelques Methodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod, Paris, 1969.

    MATH  Google Scholar 

  21. MAJDA, A.: "Equations for low Mach number combustion", (to appear in Comb. Sci. and Tech.).

    Google Scholar 

  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. MOSER, J.: "A rapidly convergent iteration method and nonlinear differential equations", Ann. Scuola Norm. Sup. Pisa 20 (1966), 265–315.

    MathSciNet  MATH  Google Scholar 

  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.

    CrossRef  Google Scholar 

  26. TEMAM, R.: The Navier-Stokes Equations, North Holland, Amsterdam, 1977.

    MATH  Google Scholar 

  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. CHORIN, A. J.: "A numerical method for solving incompressible viscous flow problems", J. Comput. Phys. 2 (1967), 12–26.

    CrossRef  ADS  MATH  Google Scholar 

  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. HALTINER, G. J. and R. T. WILLIAMS: Numerical Weather Prediction and Dynomic Meteorology, 2nd Edition, Wiley, New York, 1980.

    Google Scholar 

  31. MAJDA, A.: "The existence of multi-dimensional shock fronts", Memoirs Amer. Math. Soc. (to appear 1983).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1984 Springer-Verlag

About this chapter

Cite this chapter

Majda, A. (1984). Smooth solutions for the equations of compressible and incompressible fluid flow. In: Beirão da Veiga, H. (eds) Fluid Dynamics. Lecture Notes in Mathematics, vol 1047. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072327

Download citation

  • DOI: https://doi.org/10.1007/BFb0072327

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12893-9

  • Online ISBN: 978-3-540-38773-2

  • eBook Packages: Springer Book Archive