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Archive for Rational Mechanics and Analysis

, Volume 9, Issue 1, pp 187–195 | Cite as

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

  • James Serrin
Article

Keywords

Neural Network Complex System Weak Solution Nonlinear Dynamics Electromagnetism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Golovkin, K. K.: The plane motion of a viscous incompressible fluid. Trudy Mat. Inst. Steklov. 59, 37–86 (1960).Google Scholar
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    Hopf, E.: Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachrichten 4, 213–231 (1951).Google Scholar
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    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
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    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. [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. [6]
    Ohyama, T.: Interior regularity of weak solutions of the time dependent Navier-Stokes equation. Proc. Japan Acad. 36, 273–277 (1960).Google Scholar

Copyright information

© Springer-Verlag 1962

Authors and Affiliations

  • James Serrin
    • 1
  1. 1.Department of MathematicsInstitute of Technology University of MinnesotaMinneapolis

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