@article{AIHPC_1999__16_5_535_0,
author = {Kozono, Hideo and Sohr, Hermann},
title = {Global strong solution of the Navier-Stokes equations in 4 and 5 dimensional unbounded domains},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
volume = {16},
year = {1999},
pages = {535-561},
mrnumber = {1712576},
zbl = {0943.35067},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPC_1999__16_5_535_0}
}
Kozono, Hideo; Sohr, Hermann. Global strong solution of the Navier-Stokes equations in 4 and 5 dimensional unbounded domains. Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999) pp. 535-561. http://gdmltest.u-ga.fr/item/AIHPC_1999__16_5_535_0/
[1] and , Interpolation Spaces. Berlin-Heidelberg-New York Springer-Verlag 1976. | MR 482275 | Zbl 0344.46071
[2] and , Algebraic L2 decay for Navier-Stokes flows in exterior domains. Acta Math., Vol. 165, 1990, pp. 189-227. | MR 1075041 | Zbl 0722.35014
[3] and , L2 decay for Navier-Stokes Flows in unbounded domains, with application to exterior stationary flows. Arch. Rational Mech. Anal., Vol. 118, 1992, pp. 273-295. | MR 1158939 | Zbl 0756.76018
[4] and , On some coercive estimate for the exterior Stokes problem. Lecture Note in Math. Vol. 1530, Springer-Verlag, 1993, pp. 71-84. | MR 1226508 | Zbl 0779.35085
[5] and , On the Navier-Stokes initial value problem 1. Arch. Rational Mech. Anal., Vol. 46, 1964, pp. 269-315. | MR 166499 | Zbl 0126.42301
[6] and , On fractional power of the Stokes operators. Proc. Japan Acad., Vol. 46, 1970, pp. 1141-1143. | MR 296755 | Zbl 0235.35067
[7] , Concrete characterization of the domains of fractional powers of some elliptic differential operators of the second order. Proc. Japan Acad., Vol. 43, 1967, pp. 82-86. | MR 216336 | Zbl 0154.16201
[8] and , Monotonic decreasing and asymptotic behaviour of the kinetic energy for weak solutions of the Navier-Stokes equations in exterior domains. Arch. Rational Mech. Anal., Vol. 94, 1986, pp. 253-266. | MR 846064 | Zbl 0617.35108
[9] , Domains of fractional powers of the Stokes operator in Lr spaces. Arch. Rational Mech. Anal., Vol. 89, 1985, pp. 251-265. | MR 786549 | Zbl 0584.76037
[10] and , Solution in Lr of the Navier-Stokes initial value problem. Arch. Rational Mech. Anal., Vol. 89, 1985, pp. 267-281. | MR 786550 | Zbl 0587.35078
[11] and , On the Stokes operator in exterior domains. J. Fac. Sci. Univ. Tokyo, Sec IA, Vol. 36, 1989, pp. 103-130. | MR 991022
[12] , The Navier-Stokes equations: On the existence, regularity and decay of solutions. Indiana Univ. Math. J., Vol. 29, 1980, pp. 639-681. | MR 589434 | Zbl 0494.35077
[13] , and , On existence of solutions of the Navier-Stokes equation in a time dependent domain. J. Fac. Sci. Univ. Tokyo, Sec IA, Vol. 24, 1977, pp. 103-130. | MR 481649 | Zbl 0381.35066
[14] , Lq - Lr estimates for solutions of the nonstationary Stokes equations in an exterior domain and the Navier-Stokes initial value problems in Lq spaces. Math. Ann., Vol. 285, 1989, pp. 265-288. | MR 1016094 | Zbl 0659.35081
[15] and , Interpolation between Hp spaces: the complex method. J. Funct. Anal., Vol. 48, 1982, pp. 58-81. | MR 671315 | Zbl 0507.46047
[16] , Lp-solution of the Navier-Stokes equation in Rm, with applications to weak solutions. Math. Z., Vol. 187, 1984, pp. 471-480. | Zbl 0545.35073
[17] and , Some Lp estimate for the exterior Stokes flow and an application to the nonstationary Navier-Stokes equations. Indiana Univ. Math. J., Vol. 41, 1992, pp. 789-808. | MR 1189911 | Zbl 0759.35035
[18] and , Two-dimensional Navier-Stokes flow in unbounded domains. Math. Ann., Vol. 297, 1993, pp. 1-31. | MR 1238405 | Zbl 0796.35129
[19] and , Global strong solution and its decay properties for the Navier-Stokes equations in three dimensional domains with non-compact boundaries. Math. Z., Vol. 216, 1994, pp. 1-30. | MR 1273463 | Zbl 0798.35127
[20] , Sur le mouvement d'un liquids visqeux emplissant l'espace. Acta. Math., Vol. 63, 1994, pp. 193-248. | JFM 60.0726.05
[21] , Some results on the asymptotic behaviour of Hopf weak solutions to the Navier-Stokes equations in unbounded domains. Math. Z., Vol. 210, 1992, pp. 1-22. | MR 1161167 | Zbl 0738.35064
[22] , On the stability of incompressible viscous fluid motions past objects. J. Math. Soc. Japan, Vol. 27, 1975, pp. 294-327. | MR 440224 | Zbl 0303.76011
[23] , Weak solutions of the Navier-Stokes equations. Tohoku Math. J., Vol. 36, 1984, pp. 623-646. | MR 767409 | Zbl 0568.35077
[24] , On nonstationary solutions of the Navier-Stokes equations in an exterior domain. Hiroshima Math. J., Vol. 12, 1982, pp. 115-140. | MR 647234 | Zbl 0486.35067
[25] and , On energy inequality, smoothness and large time behavior in L2 for weak solutions of the Navier-Stokes equations in exterior domains. Math. Z., Vol. 199, 1988, pp. 455-478. | MR 968313 | Zbl 0642.35067
[26] , The initial value problem for the Navier-Stokes equations. R. E. Langer ed., University of Wisconsin Press, Madison, 1963, pp. 69-98. | MR 150444 | Zbl 0115.08502
[27] and WAHL, On the singular set and the uniqueness of weak solutions of the Navier-Stokes equations. Manuscripta Math., Vol. 49, 1984, pp. 27-59. | MR 762786 | Zbl 0567.35069
[28] , Equations of evolutions. London: Pitman 1979.
[29] , A solution formula for the Stokes equation in Rn+. Comm. Pure Appl. Math., Vol. 40, 1987, pp. 611-621. | MR 896770 | Zbl 0638.76040
[30] , The equations of Navier-Stokes and abstract parabolic equations. Braunschweig Wiesbaden: Vieweg 1985. | MR 832442