An approach to resolvent estimates for the stokes equations in Lq-spaces

  • Reinhard Farwig
  • Hermann Sohr
Problems In Unbounded Domains
Part of the Lecture Notes in Mathematics book series (LNM, volume 1530)


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  1. [1]
    Agmon, S., Douglis, A., Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I, Comm. Pure Appl. Math., 12 (1959), 623–727.MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    Bogovskii, M.E.: Solution of the first boundary value problem for the equation of continuity of an incompressible medium, Soviet Math. Dokl., 20 (1979), 1094–1098.MathSciNetGoogle Scholar
  3. [3]
    Borchers, W., Sohr, H.: On the semigroup of the Stokes operator for exterior domains in L q-spaces, Math. Z. 196 (1987), 415–425.MathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    Borchers, W., Miyakawa, T.: L 2-decay for the Navier-Stokes equations in halfspaces, Math. Ann. 282 (1988), 139–155.MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    Deuring, P.: The resolvent problem for the Stokes system in exterior domains: an elementary approach, Math. Meth. in the Appl. Sci. 13 (1990), 335–349.ADSMathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    Fujiwara, D., Morimoto, H.: An L r-theorem of the Helmholtz decomposition of vector fields, J. Fac. Sci. Univ. Tokyo, Sect. I A, 24 (1977), 685–700.MathSciNetMATHGoogle Scholar
  7. [7]
    Galdi, G.P., Simader, C.G.: Existence, uniqueness and L q-estimates for the Stokes problem in an exterior domain, Arch. Rat. Mech. Anal. 112 (1990), 291–318.MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    Giga, Y.: Analyticity of the semigroup generated by the Stokes operator in L q spaces, Math. Z. 178 (1981), 297–329.MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    Giga, Y., Sohr, H.: On the Stokes operator in exterior domains, J. Fac. Sci. Univ. Tokyo, Sect. I A, 36 (1989), 103–130.MathSciNetGoogle Scholar
  10. [10]
    Mc Cracken, M.: The resolvent problem for the Stokes equations on halfspace in L p, SIAM J. Math. Anal. 12 (1981), 221–228.MathSciNetGoogle Scholar
  11. [11]
    Miyakawa, T.: On nonstationary solutions of the Navier-Stokes equations in an exterior domain, Hiroshima Math. J. 12 (1982), 115–140.MathSciNetMATHGoogle Scholar
  12. [12]
    Simader, C.G., Sohr, H.: A new approach to the Helmholtz decomposition in L q-spaces for bounded and exterior domains, Series on Advances Mathematics for Applied Science, Vol. 11, World Scientific 1992Google Scholar
  13. [13]
    Solonnikov, V.A.: Estimates for solutions of nonstationary Navier-Stokes equations, J. Soviet Math. 8 (1977), 467–529.CrossRefMATHGoogle Scholar
  14. [14]
    Triebel, H.: Interpolation theory, function spaces, differential operators, North-Holland, Amsterdam 1978.Google Scholar
  15. [15]
    Ukai, S.: A solution formula for the Stokes equation in ℝ+n Comm. Pure Appl. Math. 40 (1987), 611–621.MathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    Wahl, von W.: Vorlesungen über das Außenraumproblem für die instationären Gleichungen von Navier-Stokes, SFB 256 Nichtlineare partielle Differentialgleichungen, Vorlesungsreihe Nr. 11, Universität Bonn 1989.Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Reinhard Farwig
    • 1
  • Hermann Sohr
    • 1
  1. 1.Fachbereich Mathematik-Informatik, Universität-GH PaderbornPaderborn

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