References
Adams, R.A.: Sobolev Spaces. New York: Academic Press 1975
Borchers, W., Miyakawa, T.:L 2 decay for the Navier-Stokes flows in unbounded domains with application to exterior stationary flows. Arch. Ration. Mech. Anal.118, 273–295 (1992)
Fujita, H., Kato, T.: On the Navier-Stokes initial value problem 1. Arch. Ration. Mech. Anal.46, 269–315 (1964)
Giga, Y., Miyakawa, T.: Solution inL r of the Navier-Stokes initial value problem. Arch. Ration. Mech. Anal.89, 267–281 (1985)
Giga, Y., Sohr, H.: On the Stokes operator in exterior domains. J. Fac. Sci. Univ. Tokyo, Sect. IA Math.36, 103–130 (1989)
Heywood, J.G.: The Navier-Stokes equations: On the existence, regularity and decay of solutions. Indiana Univ. Math. J.29, 639–681 (1980)
Itô, S.: Pn existence of Green function and positive superharmonic functions for linear elliptic operators of second order. J. Math. Soc. Japan16, 299–306 (1964)
Iwashita, H.:L q −L r estimates for solutions of nonstationary Stokes equations in an exterior domain and the Navier-Stokes initial value problem inL q spaces. Math. Ann.285, 265–288 (1989)
Kato, T., Fujita, H.: On the nonstationary Navier-Stokes system. Rend. Semin. Math., Univ. Padova32, 243–260 (1962)
Kato, T.: StrongL p-solutions of the Navier-Stokes equationR m, with applications to weak solutions. Math. Z.187, 471–480 (1984)
Kozono, H., Ogawa, T.: SomeL p estimates for the exterior Stokes flow and an application to the non-stationary Navier-Stokes equations. Indiana Univ. Math. J.41, 789–808 (1992)
Ladyzhenskaya, O.A.: The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach 1969
Maremonti, P.: Some results on the asymptotic behavior of Hopf weak solutions to the Navier-Stokes equations in unbounded domains. Math. Z.210, 1–22 (1992)
Masuda, K.: On the stability of incompressible viscous fluid motions past object. J. Math. Soc. Japan27, 294–327 (1975)
Masuda, K.: Weak solutions of the Navier-Stokes equations. Tôhoku Math. J.36, 623–646 (1984)
Miyakawa, T.: On nonstationary solutions of the Navier-Stokes equations in an exterior domain. Hiroshima Math. J.12, 115–140 (1982)
Miyakawa, T., Sohr, H.: On energy inequality, smoothness and large time behavior inL 2 for weak solutions of the Navier-Stokes equations in exterior domains. Math. Z.199, 455–478 (1988)
Reed, M., Simon, B.: Method of Modern Mathematical Physics 2, Fourier Analysis, Self Adjointness. New York: Academic Press 1975)
Serrin, J.: The initial value problem for the Navier-Stokes equations. In: Longer, R. (ed.) Nonlinear Problem, pp. 69–98. Madison: The University of Wisconsin Press 1960
Sohr, H., von Wahl, W.: On the singular set and the uniqueness of weak solutions of the Navier-Stokes equations. Manuscr. Math.49, 27–59 (1984)
Stein, E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton NJ: Princeton University Press 1970
Tanabe, H.: Equations of Evolution. London: Pitman 1979
Temam, R.: Navier-Stokes Equations. Amsterdam New York Oxford: North-Holland 1977
Ukai, S.: A solution formula for the Stokes equation inR + n. Commun. Pure Appl. Math.40, 611–621 (1987)
Wiegner, M.: Decay results for weak solutions of the Navier-Stokes equations inR n. J. Lond. Math. Soc.35, 303–313 (1987)
Wiegner, M.: Decay and stability inL p for strong solutions of the Cauchy problem for the Navier-Stokes equations. In: Heywood et al. (eds.) The Navior-Stokes equations, theory and numerical methods. (Lect. Notes Math., vol. 1431, pp. 95–99) Berlin Heidelberg New York: Springer 1988
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kozono, H., Ogawa, T. Global strong solution and its decay properties for the Navier-Stokes equations in three dimensional domains with non-compact boundaries. Math Z 216, 1–30 (1994). https://doi.org/10.1007/BF02572306
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02572306