Global strong solution of the Navier-Stokes equations in 4 and 5 dimensional unbounded domains
Annales de l'I.H.P. Analyse non linéaire, Volume 16 (1999) no. 5, p. 535-561
@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},
     publisher = {Gauthier-Villars},
     volume = {16},
     number = {5},
     year = {1999},
     pages = {535-561},
     zbl = {0943.35067},
     mrnumber = {1712576},
     language = {en},
     url = {http://www.numdam.org/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, Volume 16 (1999) no. 5, pp. 535-561. http://www.numdam.org/item/AIHPC_1999__16_5_535_0/

[1] J. Bergh and J. Löfström, Interpolation Spaces. Berlin-Heidelberg-New York Springer-Verlag 1976. | MR 482275 | Zbl 0344.46071

[2] W. Borchers and T. Miyakawa, Algebraic L2 decay for Navier-Stokes flows in exterior domains. Acta Math., Vol. 165, 1990, pp. 189-227. | MR 1075041 | Zbl 0722.35014

[3] W. Borchers and T. Miyakawa, 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] W. Borchers and T. Miyakawa, 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] H. Fujita and T. Kato, On the Navier-Stokes initial value problem 1. Arch. Rational Mech. Anal., Vol. 46, 1964, pp. 269-315. | MR 166499 | Zbl 0126.42301

[6] H. Fujita and H. Morimoto, On fractional power of the Stokes operators. Proc. Japan Acad., Vol. 46, 1970, pp. 1141-1143. | MR 296755 | Zbl 0235.35067

[7] D. Fujiwara, 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] G.P. Galdi and P. Maremonti, 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] Y. Giga, 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] Y. Giga and T. Miyakawa, 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] Y. Giga and H. Sohr, On the Stokes operator in exterior domains. J. Fac. Sci. Univ. Tokyo, Sec IA, Vol. 36, 1989, pp. 103-130. | MR 991022

[12] J.G. Heywood, 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] A. Inoue, and M. Wakimoto, 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] H. Iwashita, 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] S. Janson and P.W. Jones, Interpolation between Hp spaces: the complex method. J. Funct. Anal., Vol. 48, 1982, pp. 58-81. | MR 671315 | Zbl 0507.46047

[16] T. Kato, 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] H. Kozono and T. Ogawa, 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] H. Kozono and T. Ogawa, Two-dimensional Navier-Stokes flow in unbounded domains. Math. Ann., Vol. 297, 1993, pp. 1-31. | MR 1238405 | Zbl 0796.35129

[19] H. Kozono and T. Ogawa, 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] J. Leray, Sur le mouvement d'un liquids visqeux emplissant l'espace. Acta. Math., Vol. 63, 1994, pp. 193-248. | JFM 60.0726.05

[21] P. Maremonti, 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] K. Masuda, 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] K. Masuda, Weak solutions of the Navier-Stokes equations. Tohoku Math. J., Vol. 36, 1984, pp. 623-646. | MR 767409 | Zbl 0568.35077

[24] T. Miyakawa, 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] T. Miyakawa and H. Sohr, 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] J. Serrin, 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] H. Sohr and W. Von 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] H. Tanabe, Equations of evolutions. London: Pitman 1979.

[29] S. Ukai, 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] W. Von Wahl, The equations of Navier-Stokes and abstract parabolic equations. Braunschweig Wiesbaden: Vieweg 1985. | MR 832442