Skip to main content
SpringerLink
Log in

On the interior regularity of weak solutions of the Navier-Stokes equations

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Golovkin, K. K.: The plane motion of a viscous incompressible fluid. Trudy Mat. Inst. Steklov. 59, 37–86 (1960).

    Google Scholar 

  2. Hopf, E.: Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachrichten 4, 213–231 (1951).

    Google Scholar 

  3. Kiselev, A. A., & O. A. Ladyshenskaya: On existence and uniqueness of the solution of the nonstationary problem for a viscous incompressible fluid. Izvestiya Akad. Nauk SSSR 21, 655–680 (1957).

    Google Scholar 

  4. Ladyshenskaya, O. A.: Solution “in the large” of the nonstationary boundary value problem for the Navier-Stokes System with two space variables. Comm. Pure Appl. Math. 12, 427–433 (1959).

    Google Scholar 

  5. Lions, J. L., & G. Prodi: Un théorème d'existence et unicité dans les équations de Navier-Stokes en dimension 2. C. R. Acad. Sci., Paris 248, 3519–3521 (1959).

    Google Scholar 

  6. Ohyama, T.: Interior regularity of weak solutions of the time dependent Navier-Stokes equation. Proc. Japan Acad. 36, 273–277 (1960).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Institute of Technology University of Minnesota, Minneapolis, Minnesota

    James Serrin

Authors
  1. James Serrin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The above research was supported by the United States Air Force under Contract No. AF 49(638)-262, and also by the Office of Naval Research under Contract No. 225(11) with Stanford University.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Serrin, J. On the interior regularity of weak solutions of the Navier-Stokes equations. Arch. Rational Mech. Anal. 9, 187–195 (1962). https://doi.org/10.1007/BF00253344

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00253344

Keywords

Search

Navigation