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On stationary solutions of the Navier-Stokes equations as limits of nonstationary solutions

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References

  1. Ladyzhenskaya, O.A., The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach 1963.

    Google Scholar 

  2. Finn, R., On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems. Arch. Rational Mech. Anal. 19, 363–406 (1965).

    Google Scholar 

  3. Finn, R., Stationary solutions of the Navier-Stokes equations. Proc. Symp. Appl. Math. 19, Amer. Math. Soc. (1965).

  4. Finn, R., On steady-state solutions of the Navier-Stokes partial differential equations. Arch. Rational Mech. Anal. 3, 381–396 (1959).

    Google Scholar 

  5. Finn, R., On the steady-state solutions of the Navier-Stokes equations, III. Acta Math. 105, 197–244 (1961).

    Google Scholar 

  6. Leray, J., Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'Hydrodynamique. J. Math. Pures Appl. 9, 1–82 (1933); Les problèmes non linéaires, Enseignement Math. 35, 139–151 (1936).

    Google Scholar 

  7. Smith, D. R., Estimates at infinity for stationary solutions of the Navier-Stokes equations in two dimensions. Arch. Rational Mech. Anal. 20, 341–372 (1965).

    Google Scholar 

  8. Finn, R., & D.R. Smith, On the stationary solutions of the Navier-Stokes equations in two dimensions. Arch. Rational Mech. Anal. 25, 26–39 (1967).

    Google Scholar 

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

    Google Scholar 

  10. Serrin, J., On the interior regularity of weak solutions of the Navier-Stokes equations. Arch. Rational Mech. Anal. 9, 187–195 (1962).

    MATH  Google Scholar 

  11. Hopf, E., Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachr. 4, 213–231 (1951).

    MathSciNet  MATH  Google Scholar 

  12. Agmon, S., Lectures on Elliptic Boundary Value Problems. Princeton, N.J.: Van Nostrand 1965.

    Google Scholar 

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Communicated by J. L. Lions

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Heywood, J.G. On stationary solutions of the Navier-Stokes equations as limits of nonstationary solutions. Arch. Rational Mech. Anal. 37, 48–60 (1970). https://doi.org/10.1007/BF00249501

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