Skip to main content
Log in

Variational principles and generalized variational principles in hydrodynamics of viscous fluids

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

In this paper, the variational principles of hydrodynamic problems for the incompressible and compressible viscous fluids are established. These principles are principles of maximum power losses. Their generalized variational principles are also discussed on the basis of Lagrangian multiplier methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Lin,C.C. and L.Rubinov, On the flow behind curved shocks, Journal of Mathematics and Physics, Vol. 27, (1948), 105–129.

    Google Scholar 

  2. Skobeikin,V.I., Variational principles in hydrodynamics, Soviet Physics JETP, Vol. 4, No. 1, (1957), 68–71.

    Google Scholar 

  3. Guderley,K.G., An extremum principle for three-dimensional compressible inviscid flows, SIAM, Journal of Applied Mathematics, Vol. 23, No. 2, (1972), 259–275.

    Google Scholar 

  4. Morice,P., Un Principe Variational et ume Méthode de Résolution Numérique par Elements Finis pour des Ecoulements Avec Frontiers Libres, Paper presented at XIII Symposium of Dynamics of Fluids, Kortawo, Poland, Sept. (1977).

  5. Manwell,A.R., A variational principle for steady Honenergie compressible flow with finite shocks, Wave Motion, Vol. 2, (1980), 83–95.

    Google Scholar 

  6. Hafez,M. and D.Lovell, Numerical solution of transonic stream function equation, AIAA Journal, Vol. 21, No. 3, (1983).

  7. Chien,W.Z., Method of high-order Lagrange multiplier and generalized variational principles of elasticity with more general forms of functionals, Applied Mathematics and Mechanics, Vol. 4, No. 2, (1983), 143–157.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wei-zang, C. Variational principles and generalized variational principles in hydrodynamics of viscous fluids. Appl Math Mech 5, 1281–1296 (1984). https://doi.org/10.1007/BF01904951

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01904951

Keywords

Navigation