Skip to main content
Log in

Non stationary Navier-Stokes flows with vanishing viscosity

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Summary

An elementary proof that the solution of the Cauchy problem for the Navier-Stokes equations converges, in an appropriate sense, to the solution of the Euler equations on a small time interval is given. A partial result is given in the case of initial boundary-value problems.

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. Aubin J. P.,Un théoreme de compacité, C. R. Acad. Sc. Paris,256 (1963), 5042–5044.

    MATH  MathSciNet  Google Scholar 

  2. Ebin D. G. and Marsden J. E.,Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math., (2)97 (1970), 102–163.

    Article  MathSciNet  Google Scholar 

  3. Golovkin K. K.,New equations modeling the motion of a viscous fluid and their unique solvability, Trudy Mat. Inst. Steklov,102 (1967), 29–50; Proc. Steklov Inst. Math.,102 (1967), 29–54.

    MathSciNet  Google Scholar 

  4. Kato T.,Non stationary flows of viscous and ideal flows in R 3, J. Functional Analysis, (1972), 296–305.

  5. Ladyzenskaya O. A.,New equations for the description of motion of viscous incompressible fluids and solvability in the large of boundary-value problems for them, Trudy Mat. Inst. Steklov102 (1967), 85–104; Proc. Steklov Inst. Math.102 (1967) 95–118.

    MathSciNet  Google Scholar 

  6. —,The Mathematical theory of viscous incompressible fluids, Gordon and Breach, New York, 1969.

    Google Scholar 

  7. Lions J. L.,Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969.

    MATH  Google Scholar 

  8. Swann H. S. G.,The convergence with vanishing viscosity of non stationary Navier-Stokes flow to ideal flow in R 3. Trans. Amer. Math. Soc.157 (1971), 373–397.

    Article  MATH  MathSciNet  Google Scholar 

  9. Visik M. I.,Quasi-linear strongly elliotic systems of differential equations in divergence form, Trudy Moskov Math. Obsc.12, (1963), 125 184; Trans. Moscov Math. Soc (1963), 140–208.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ton, B.A. Non stationary Navier-Stokes flows with vanishing viscosity. Rend. Circ. Mat. Palermo 27, 113–129 (1978). https://doi.org/10.1007/BF02843932

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02843932

Keywords

Navigation