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The exterior problem for the stationary Navier-Stokes equations: On the existence and regularity

  • 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. Agmom, S., Douglis, A., Niremberg, L.: Estimates near the boundary of elliptic differential equations satisfying general boundary conditions II. Comm. Pure Appl. Math. 17 (1964), 35–92.

    Article  MathSciNet  Google Scholar 

  2. Babenko, K.I.: On stationary solutions of the problem of flow past a body of viscous incompressible fluid. Math. USSR Sbornik 20 (1973), 1–25.

    Article  MathSciNet  MATH  Google Scholar 

  3. Bemelmans, J.: Eine Außenraumaufgabe fur die instationaren Navier-Stokes Gleichungen. Math. Z. 162 (1978), 145–173.

    Article  MathSciNet  MATH  Google Scholar 

  4. Cattabriga, L.: Su un problema al contorno relativo al sistema di equazioni di Stokes. Rend. Sem. Mat. Univ. Padova 31 (1961), 308–340.

    MathSciNet  MATH  Google Scholar 

  5. Farwig, R.: The stationary exterior 3D-problem of Oseen and Navier-Stokes equations in anisotropically weighted Sobolev spaces, Preprint.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Finn, R.: On the exterior stationary problem for the Navier-Stokes equations, and associated pertubation problems. Arch. Rat. Mech. Anal. 19 (1965), 363–406.

    Article  MathSciNet  MATH  Google Scholar 

  8. Fujita, H.: On the existence and regularity of the steady-state solutions of the Navier-Stokes equations. J. Fac. Sci. Univ. Tokyo 9 (1961), 59–102.

    MATH  Google Scholar 

  9. Galdi, P.G.: Existence, Uniqueness and Lq-estimates for the Stokes problem in an exterior domain. Preprint.

    Google Scholar 

  10. Ladyzhenskaya, O. A.: The mathematical theory of viscous incompressible flow. Gordon & Breach, New York 1969.

    MATH  Google Scholar 

  11. Leray, J.: Etude de diverses equations integrales non lineaires et de quelques problemes que pose l'hydrodynamique. J. Math. Pures Appl. 12 series 9 (1933), 1–82.

    MathSciNet  MATH  Google Scholar 

  12. Mizumachi, R.: On the asymptotic behavior of incompressible viscous fluid motions past bodies. J. Math. Soc. Japan. 36 (1984), 497–522.

    Article  MathSciNet  MATH  Google Scholar 

  13. Oseen, C.W.: Neure Methoden und Ergebnisse in der Hydrodynamik. Akademische Verlagsgesellschaft, Leipzig 1927.

    MATH  Google Scholar 

  14. Solonnikov, V.A.: Estimates of the solutions of a nonstationary linearized system of Navier-Stokes equations. Amer. Math. Soc. Transl. (2) 75 (1968) 1–116.

    Article  MATH  Google Scholar 

  15. Solonnikov, V.A.: Estimates of solutions of an initial-boundary value problem for the linear nonstationary Navier-Stokes system. J. Sov. Math. (1978) 336–389.

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Rodolfo Salvi

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  1. Rodolfo Salvi
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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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Salvi, R. (1992). The exterior problem for the stationary Navier-Stokes equations: On the existence and regularity. 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/BFb0090338

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  • DOI: https://doi.org/10.1007/BFb0090338

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56261-0

  • Online ISBN: 978-3-540-47498-2

  • eBook Packages: Springer Book Archive

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