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Lp estimates for the stokes system

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Functional Analysis and Related Topics, 1991

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1540))

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References

  1. W. Borchers and T. Miyakawa, Algebraic L 2-decay for Navier-Stokes flows in exterior domains, Acta Math. 165 (1990), 89–227.

    Article  MathSciNet  MATH  Google Scholar 

  2. D.L. Burkholder, Explorations in martingale theory and its applications, Ecole d'Ete de Probabilités de Saint-Flour XIX-1989, Lecture Notes in Math. 1464 (1991), 1–66. (ed. P.L. Hennequin), Springer.

    Google Scholar 

  3. P. Butzer and H. Berens, Semi-Groups of Operators and Approximations, Berlin-Heidelberg-New York (1967).

    Google Scholar 

  4. G. Dore and A. Venni, On the closedness of the sum of two closed operators, Math. Z. 196 (1987), 189–201.

    Article  MathSciNet  MATH  Google Scholar 

  5. _____, Maximal regularity for parabolic initial-boundary value problems in Sobolev spaces, Math. Z. 208 (1991), 297–308.

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Giga, Y. Giga and H. Sohr, L p estimate for abstract linear parabolic equations, Proc. Japan Acad. 67 (1991), 197–202.

    Article  MathSciNet  MATH  Google Scholar 

  7. Y. Giga, Domains of fractional powers of the Stokes operators in L r spaces, Arch. Rational Mech. Anal. 89 (1985), 251–265.

    Article  MathSciNet  MATH  Google Scholar 

  8. Y. Giga and H. Sohr, On the Stokes operator in exterior domains, J. Fac. Sci. Univ. Tokyo Sec. IA36 (1989), 103–130.

    MathSciNet  Google Scholar 

  9. _____, Abstract L p estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains, J. Func. Anal. 102 (1991), 72–94.

    Article  MathSciNet  MATH  Google Scholar 

  10. T. Kato, Note on fractional powers of linear operators, Proc. Japan Acad. 36 (1960), 94–96.

    Article  MathSciNet  MATH  Google Scholar 

  11. H. Komatsu, Fractional powers of operators, Pacific J. Math. 19 (1966), 285–346.

    Article  MathSciNet  MATH  Google Scholar 

  12. S. Krein, Linear Differential Equations in Banach Spaces, Amer. Math. Soc., Providence, 1972.

    Google Scholar 

  13. J. Prüss and H. Sohr, On operators with bounded imaginary powers in Banach spaces, Math. Z. 203 (1990), 429–452.

    Article  MathSciNet  MATH  Google Scholar 

  14. M. Reed and B. Simon, Methods of Mordern Mathematical Physics vol. II, Academic Press, New York-San Francisco-London 1975.

    Google Scholar 

  15. H. Tribel, Interpolation Theory, Function Spaces, Differential Operators. North-Holland-Amsterdam-New York-Oxford (1978).

    Google Scholar 

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Hikosaburo Komatsu

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© 1993 Springer-Verlag

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Giga, M., Giga, Y., Sohr, H. (1993). Lp estimates for the stokes system. In: Komatsu, H. (eds) Functional Analysis and Related Topics, 1991. Lecture Notes in Mathematics, vol 1540. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085474

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  • DOI: https://doi.org/10.1007/BFb0085474

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56471-3

  • Online ISBN: 978-3-540-47565-1

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