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Adams, R. A., Sobolev Spaces, Academic Press, New York, 1975.
Agmon, S., On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math. 15 (1962), 119–147.
Borchers, W. & Miyakawa, T., Algebraic L 2 decay for Navier-Stokes flows in exterior domains, Acta Math. 165 (1990), 189–227.
Borchers, W. & Sohr, H., On the semigroup of the Stokes operator for exterior domains in L q-spaces, Math. Z. 196 (1987), 415–425.
Finn, R., On exterior stationary problem for the Navier-Stokes equations and associated perturbation problems., Arch. Rational Mech. Anal. 19 (1965), 363–406.
Fujita, H. & Kato, T., On the Navier-Stokes initial value problem 1, Arch. Rational Mech. Anal. 46 (1964), 269–315.
Fujiwara, D., L p-theory for characterizing the domain of fractional powers of — Δ in the half space, J. Fac. Sci. Univ. Tokyo, Sec I. 15 (1965), 169–177.
Fujiwara, D. & Morimoto, H., An L r-theorem of the Helmholtz decomposition of vector fields, J. Fac. Sci. Univ. Tokyo, Sec I. 24 (1977), 685–700.
Galdi, G. P. & Padula, M., Existence of steady incompressible flows past an obstacle, preprint.
Giga, Y., Analyticity of the semigroups generated by the Stokes operator in L r spaces, Math. Z. 178 (1981), 297–329.
Giga, Y., Domains of fractional powers of the Stokes operator in L r spaces, Arch. Rational Mech. Anal. 89 (1985), 251–265.
Giga, Y. & Miyakawa, T., Solution in L r of the Navier-Stokes initial value problem, Arch. Rational Mech. Anal. 89 (1985), 267–281.
Giga, Y. & Sohr, H., On the Stokes operator in exterior domains, J. Fac. Sci. Univ. Tokyo, Sec I. 36 (1989), 103–130.
Heywood, J. G., On stationary solutions of the Navier-Stokes equations as limits of nonstationary solutions, Arch. Rational Mech. Anal. 37 (1970), 48–60.
Heywood, J. G., The Navier-Stokes equations: On the existence, regularity and decay of solutions, Indiana Univ. Math. J. 29 (1980), 639–681.
Iwashita, H., L q -L r estimates for solutions of the nonstationary Stokes equations in an exterior domain and the Navier-Stokes initial value problems in L q spaces, Math. Ann. 285 (1989), 265–288.
Kato, T. & Fujita, H., On the nonstationary Navier-Stokes system, Rend. Sem. Math. Univ. Padova 32 (1962), 243–260.
Kato, T., Perturbation Theory for Linear Operators, Springer-Verlag, Berlin-Heidelberg-New York, 1966.
Kato, T., Strong L p-solution of the Navier-Stokes equation in R m, with applications to weak solutions, Math. Z. 187 (1984), 471–480.
Kozono, H., Global L n-solution and its decay property for the Navier-Stokes equations in half-space R n+ , J. Diff. Eqs 79 (1989), 79–88.
Kozono, H. & Sohr, H., On a new class of generalized solutions for the Stokes equations in exterior domains, Ann. Scuola Norm. Sup. Pisa 19 (1992), 155–181.
Kozono, H. & Sohr, H., On stationary Navier-Stokes equations in unbounded domains, Ricerche Mat. 42 (1993), 69–86.
Kozono, H. & Sohr, H., Density properties for solenoidal vector fields, with applications to the Navier-Stokes equations in exterior domains, J. Math. Soc. Japan 44 (1992), 307–330.
Ladyzhenskaya, O. A., The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York, 1969.
Masuda, K., On the stability of incompressible viscous fluid motions past object, J. Math. Soc. Japan 27 (1975), 294–327.
Masuda, K., Weak solutions of the Navier-Stokes equations, Tohoku Math. J. 36 (1984), 623–646.
Miyakawa, T., On nonstationary solutions of the Navier-Stokes equations in an exterior domain, Hiroshima Math. J. 12 (1982), 115–140.
Schonbek, M. E., L 2 decay for weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal. 88 (1985), 209–222.
Secchi, P., On the stationary and nonstationary Navier-Stokes equations in R n, Ann. Mat. Pura Appl. 153 (1988), 293–306.
Serrin, J., The initial value problem for the Navier-Stokes equations, Nonlinear Problems, R. Langer, ed., The University of Wisconsin Press, Madison, 1960, pp. 69–98.
Simader, C. G. & Sohr, H., A new approach to the Helmholtz decomposition and the Neumann problem in L q-spaces for bounded and exterior domains, Mathematical Problems Relating to the Navier-Stokes Equations, series on Advanced in Mathematics for Applied Sciences, G. P. Galdi ed., (1992), 1–35, World Scientific, Singapore-New Jersey-London-Hong Kong.
Solonnikov, V. A., Estimates for solutions of nonstationary Navier-Stokes equations, J. Sov. Math. 8 (1977), 467–529.
Tanabe, H., Equations of Evolution, Pitman, London, 1979.
Teman, R., Navier-Stokes Equations, North-Holland, Amsterdam, New York, Oxford, 1977.
Ukai, S., A solution formula for the Stokes equation in R n+ , Comm. Pure Appl. Math. 40 (1987), 611–621.
von Wahl, W., The equations of Navier-Stokes and abstract parabolic equations, Vieweg, Braunschweig-Wiesbaden, 1985.
Wiegner, M., Decay results for weak solutions of the Navier-Stokes equations in R n, J. London Math. Soc. 35 (1987), 303–313.
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Communicated by H. Brezis
Dedicated to Professor Yoshio Kato on his sixtieth birthday
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Kozono, H., Ogawa, T. On stability of Navier-Stokes flows in exterior domains. Arch. Rational Mech. Anal. 128, 1–31 (1994). https://doi.org/10.1007/BF00380792
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DOI: https://doi.org/10.1007/BF00380792