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Some results on the asymptotic behaviour of solutions to the Navier-Stokes equations

  • Problems In Unbounded Domains
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The Navier-Stokes Equations II — Theory and Numerical Methods

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1530))

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References

  1. L. Caffarelli, R. Kohn and L. Nirenberg. Partial regularity of suitable weak solutions of the Navier-Stokes equations, Comm. Pure Appl. Math XXXV (1982) 771–831.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. R. Kayikiya and T. Miyakawa. On the L 2 decay of weak solutions of the Navier-Stokes equations in ℝn. Math. Z. 192 (1986) 135–148.

    Article  MathSciNet  Google Scholar 

  3. P. Galdi, P. Maremonti. Navier-Stokes equations in exterior domains. Archive for Rational Mechanics 94 (1986) 253–266.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. T. Kato. Non-stationary flows of viscous and ideal fluids in ℝ3. Journal of Functional Analysis 9 (1972) 295–305.

    Article  Google Scholar 

  5. J. Leray. Sur le mouvement d'une liquide visqueux complissent l'espace. Acta Math 63, 1934, 193–248.

    Article  MathSciNet  Google Scholar 

  6. M. E. Schonbek, L 2 decay for weak solutions of the Navier-Stokes equations, Archive for Rational Mechanics and Analysis, Vol. 88, 3, 1985, pp. 209–222.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. M. E. Schonbek. Large time behavior of solutions to the Navier-Stokes equations, Comm. in P.D.E. 11(7) (1986) 753–763.

    Article  MathSciNet  Google Scholar 

  8. M. E. Schonbek. Lower bounds of rates of decay for solutions to the Navier-Stokes equations. Journal of American Mathematical Society, July 1991.

    Google Scholar 

  9. M. E. Schonbek. Asymptotic behaviour of solutions to the three-dimensional Navier-Stokes equation. Preprint.

    Google Scholar 

  10. Temam. Navier-Stokes Equations, Theory and Numerical Analysis. North Holland, Amsterdam and NY. 1972.

    Google Scholar 

  11. M. Wiegner. Decay results for weak solutions of the Navier-Stokes equations in ℝn. J. London Math Soc. 35 (1987) 303–313.

    Article  MathSciNet  MATH  Google Scholar 

  12. M. Wiegner. Some remarks concerning the approximation of weak solutions in exterior domains for n=3,4. Private communication.

    Google Scholar 

  13. M. von Wahl. The equations of Navier-Stokes and abstract parabolic equations. Aspects of Mathematics (Viewig-Verlag 1985).

    Google Scholar 

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John G. Heywood Kyûya Masuda Reimund Rautmann Vsevolod A. Solonnikov

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© 1992 Springer-Verlag

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Schonbek, M.E. (1992). Some results on the asymptotic behaviour of solutions to the Navier-Stokes equations. In: Heywood, J.G., Masuda, K., Rautmann, R., Solonnikov, V.A. (eds) The Navier-Stokes Equations II — Theory and Numerical Methods. Lecture Notes in Mathematics, vol 1530. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090339

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  • DOI: https://doi.org/10.1007/BFb0090339

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56261-0

  • Online ISBN: 978-3-540-47498-2

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