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Agmon, S., Douglis, A., Nirenberg, L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II. Commun. Pure Appl. Math.17, 35–92 (1964)
Caffarelli, L., Kohn, R., Nirenberg, L.: Partial regularity for suitable weak solutions of the Navier-Stokes equations. Commun. Pure Appl. Math.35, 771–831 (1982)
Friedman, A.: Partial differential equations. New York: Holt, Rinehart & Winston 1969
Fujiwara, D., Morimoto, H.: AnL r-theorem of the Helmholtz decomposition of vector fields. J. Fac. Sci., Univ. Tokyo, Sect. I A24, 685–700 (1977)
Giga, Y.: Domains of fractional powers of the Stokes operator inL r spaces. Arch. Rat. Mech. Anal.89, 251–265 (1985)
Hörmander, L.: Estimates for translation invariant operators inL p spaces. Acta Math.194, 93–139 (1960)
Kajikiya, R., Miyakawa, T.: OnL 2 decay of weak solutions of the Navier-Stokes equations inR n. Math. Z.192, 135–148 (1986)
Leray, J.: Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math.63, 193–248 (1934)
McCracken, M.: The resolvent problem for the Stokes equation on halfspaces inL p. SIAM J. Math. Anal.12, 201–228 (1981)
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. (to appear)
Reed, M., Simon, B.: Methods of modern mathematical physics II; Fourier analysis, selfadjointness. New York London San Francisco: Academic Press 1975
De Rham, G.: Variétés différentiables. Paris: Hermann 1955
Schonbek, M.E.:L 2 decay for weak solutions of the Navier-Stokes equations. Arch. Rat. Mech. Anal.88, 209–222 (1985)
Schonbek, M.E.: Large time behaviour of solutions to the Navier-Stokes equations. Commun. Partial Differ. Equations11, 733–763 (1986)
Sohr, H., Wahl, W. von, Wiegner, M.: Zur Asymptotik der Gleichungen von Navier-Stokes. Nachr. Akad. Wiss. Gött., II. Math.-Phys. Kl.3, 45–59 (1986)
Solonnikov, V.A.: Estimates for solutions of nonstationary Navier-Stokes equations. J. Sov. Math.8, 467–529 (1977)
Stein, E.: Singular integrals and differentiability properties of functions. Princeton: Princeton University Press 1970
Tanabe, H.: Equations of evolution. London: Pitman 1979
Temam, R.: Navier-Stokes equations. Amsterdam: North-Holland 1977
Ukai, S.: A solution formula for the Stokes equation inR + n. Commun. Pure Appl. Math.49, 611–621 (1987)
Wahl, W. von: Regularitätsfragen für die instationären Navier-Stokesschen Gleichungen in höheren Dimensionen. J. Math. Soc. Japan32, 263–283 (1980)
Wiegner, M.: Decay results for weak solutions of the Navier-Stokes equations inR n. J. London Math. Soc.35, 303–313 (1987)
Simader, C.G., Sohr, H.: The Helmholtz decomposition inL q and related topics. Preprint
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Supported in part by the Alexander von Humboldt Research Fellowship
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Borchers, W., Miyakawa, T. L 2 decay for the Navier-Stokes flow in halfspaces. Math. Ann. 282, 139–155 (1988). https://doi.org/10.1007/BF01457017
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DOI: https://doi.org/10.1007/BF01457017