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Acta Applicandae Mathematica

, Volume 37, Issue 1–2, pp 53–66 | Cite as

Weighted estimates for stationary Navier-Stokes equations

  • Jens Frehse
  • Michael RüŽička
Article

Abstract

We show Morrey-type estimates for the weak solution of the periodic Navier-Stokes equations in dimensionN, 5 <N < 10. ForN < 8, we prove the existence of a ‘maximum solution’.

Mathematics subject classification (1991)

35B30 35J60 76D05 

Key words

a-priori estimates regularity maximum property Navier-Stokes equations 

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References

  1. 1.
    Caffarelli, L., Kohn, R. and Nirenberg, L.: Partial regularity of suitable weak solutions of the Navier-Stokes equationsComm. on Pure and Appl. Math. 35 (1985), 771–831.Google Scholar
  2. 2.
    Frehse, J. and RůŽička, M.: On the regularity of the stationary Navier-Stokes equations,Ann. Scu. Norm. Pisa, Ser IV 21(1) (1994), 63–95.Google Scholar
  3. 3.
    Gerhardt, C.: Stationary solutions to the Navier-Stokes equations in dimension four,Math. Zelt. 165 (1979), 193–197.Google Scholar
  4. 4.
    Gilbarg, D. and Trudinger, N. S.:Elliptic Partial Differential Equations of Second Order, Springer, New York, 1983.Google Scholar
  5. 5.
    Struwe, M.: On partial regularity results for the Navier-Stokes equations,Comm. Pure Appl. Math. 41 (1988), 437–458.Google Scholar
  6. 6.
    Temam, R.:Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer, New York, 1988.Google Scholar
  7. 7.
    Frehse, J. and RůŽička, M.: Regularity for the stationary Navier-Stokes equations in bounded domains (to appear inArch. Rational Mech. Anal.).Google Scholar
  8. 8.
    Frehse, J. and RůŽička, M.: Existence of regular solutions to the stationary Navier-Stokes equations (to appear inMath. Ann.).Google Scholar
  9. 9.
    Struwe, M.: Regular solutions of the stationary Navier-Stokes equations on ℝ5 (to appear inMath. Ann.).Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Jens Frehse
    • 1
  • Michael RüŽička
    • 1
  1. 1.Institute of Applied MathematicsUniversity BonnBonnGermany

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