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) no. 5, pp. 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},
     pages = {535--561},
     publisher = {Gauthier-Villars},
     volume = {16},
     number = {5},
     year = {1999},
     mrnumber = {1712576},
     zbl = {0943.35067},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1999__16_5_535_0/}
}
TY  - JOUR
AU  - Kozono, Hideo
AU  - Sohr, Hermann
TI  - Global strong solution of the Navier-Stokes equations in 4 and 5 dimensional unbounded domains
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1999
SP  - 535
EP  - 561
VL  - 16
IS  - 5
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPC_1999__16_5_535_0/
LA  - en
ID  - AIHPC_1999__16_5_535_0
ER  - 
%0 Journal Article
%A Kozono, Hideo
%A Sohr, Hermann
%T Global strong solution of the Navier-Stokes equations in 4 and 5 dimensional unbounded domains
%J Annales de l'I.H.P. Analyse non linéaire
%D 1999
%P 535-561
%V 16
%N 5
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPC_1999__16_5_535_0/
%G en
%F 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) 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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[15] S. Janson and P.W. Jones, Interpolation between Hp spaces: the complex method. J. Funct. Anal., Vol. 48, 1982, pp. 58-81. | MR | Zbl

[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

[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 | Zbl

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

[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 | Zbl

[20] J. Leray, Sur le mouvement d'un liquids visqeux emplissant l'espace. Acta. Math., Vol. 63, 1994, pp. 193-248. | JFM

[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 | Zbl

[22] K. Masuda, On the stability of incompressible viscous fluid motions past objects. J. Math. Soc. Japan, Vol. 27, 1975, pp. 294-327. | MR | Zbl

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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