Skip to main content
SpringerLink
Log in

A spatial decay estimate for the Navier-Stokes equations

  • Original Papers
  • Published:
Zeitschrift für angewandte Mathematik und Physik ZAMP Aims and scope Submit manuscript

Abstract

An expression for the spatial decay of an energy functional of solutions of the Navier-Stokes equations is given. The decay is exponential in nature with a decay constant which depends only on the geometry of the flow region.

Résumé

Nous exprimons la diminution par rapport à la distance d'une fonction d'énergie de certaines solutions des équations de Navier-Stokes. L'expression est du type exponentiel décroissant dont le coefficient ne dépend que de la forme de la région d'écoulement.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. H. Bramble andL. E. Payne,Bounds in the Neumann Problem for Second Order Uniformly Elliptic Operators, Pacific J. Math.12, 823–833 (1962).

    Google Scholar 

  2. W. S. Edelstein,A Spatial Decay Estimate for the Heat Equation, Z. angew. Math. Phys.20, 900–906 (1969).

    Google Scholar 

  3. D. D. Joseph,Stability of Fluid Motions, Vol. I, Springer-Verlag, New York and Heidelberg (1976).

    Google Scholar 

  4. L. E. Payne,Uniqueness Criteria for Steady State Solutions of the Navier-Stokes Equations, Atti del Simp. Inter. sulle Appl. dell' Anal. alla Fis. Mat., Cagliari-Sassari,28, 130–153 (1964).

    Google Scholar 

  5. V. G. Sigillito,On the Spatial Decay of Solutions of Parabolic Equations, Z. angew. Math. Phys.21, 1078–1081 (1970).

    Google Scholar 

  6. E. M. Stein,Singular Integrals and the Differentiability Properties of Functions, Princeton University Press, Princeton, N. J. (1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept of Mathematics, Wichita State University, Wichita, Kansas

    Alan R. Elcrat

  2. Applied Physics Laboratory, The Johns Hopkins University, Laurel, Maryland, USA

    Vincent G. Sigillito

Authors
  1. Alan R. Elcrat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vincent G. Sigillito
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported in part by the Department of the Navy, Naval Sea Systems Command, under Contract No. N00024-78-C-5384.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Elcrat, A.R., Sigillito, V.G. A spatial decay estimate for the Navier-Stokes equations. Journal of Applied Mathematics and Physics (ZAMP) 30, 449–455 (1979). https://doi.org/10.1007/BF01588889

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01588889

Keywords

Search

Navigation