Global strong solution of the Navier-Stokes equations in 4 and 5 dimensional unbounded domains

 Access to full text

 Full (PDF)

1. [1] J. Bergh and J. Löfström, Interpolation Spaces. Berlin-Heidelberg-New YorkSpringer-Verlag1976. Zbl0344.46071MR482275
2. [2] W. Borchers and T. Miyakawa, Algebraic L2 decay for Navier-Stokes flows in exterior domains. Acta Math., Vol. 165, 1990, pp. 189-227. Zbl0722.35014MR1075041
3. [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. Zbl0756.76018MR1158939
4. [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. Zbl0779.35085MR1226508
5. [5] H. Fujita and T. Kato, On the Navier-Stokes initial value problem 1. Arch. Rational Mech. Anal., Vol. 46, 1964, pp. 269-315. Zbl0126.42301MR166499
6. [6] H. Fujita and H. Morimoto, On fractional power of the Stokes operators. Proc. Japan Acad., Vol. 46, 1970, pp. 1141-1143. Zbl0235.35067MR296755
7. [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. Zbl0154.16201MR216336
8. [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. Zbl0617.35108MR846064
9. [9] Y. Giga, Domains of fractional powers of the Stokes operator in Lr spaces. Arch. Rational Mech. Anal., Vol. 89, 1985, pp. 251-265. Zbl0584.76037MR786549
10. [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. Zbl0587.35078MR786550
11. [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. MR991022
12. [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. Zbl0494.35077MR589434
13. [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. Zbl0381.35066MR481649
14. [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. Zbl0659.35081MR1016094
15. [15] S. Janson and P.W. Jones, Interpolation between Hp spaces: the complex method. J. Funct. Anal., Vol. 48, 1982, pp. 58-81. Zbl0507.46047MR671315
16. [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. Zbl0545.35073
17. [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. Zbl0759.35035MR1189911
18. [18] H. Kozono and T. Ogawa, Two-dimensional Navier-Stokes flow in unbounded domains. Math. Ann., Vol. 297, 1993, pp. 1-31. Zbl0796.35129MR1238405
19. [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. Zbl0798.35127MR1273463
20. [20] J. Leray, Sur le mouvement d'un liquids visqeux emplissant l'espace. Acta. Math., Vol. 63, 1994, pp. 193-248. JFM60.0726.05
21. [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. Zbl0738.35064MR1161167
22. [22] K. Masuda, On the stability of incompressible viscous fluid motions past objects. J. Math. Soc. Japan, Vol. 27, 1975, pp. 294-327. Zbl0303.76011MR440224
23. [23] K. Masuda, Weak solutions of the Navier-Stokes equations. Tohoku Math. J., Vol. 36, 1984, pp. 623-646. Zbl0568.35077MR767409
24. [24] T. Miyakawa, On nonstationary solutions of the Navier-Stokes equations in an exterior domain. Hiroshima Math. J., Vol. 12, 1982, pp. 115-140. Zbl0486.35067MR647234
25. [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. Zbl0642.35067MR968313
26. [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. Zbl0115.08502MR150444
27. [27] H. Sohr and W. VonWAHL, On the singular set and the uniqueness of weak solutions of the Navier-Stokes equations. Manuscripta Math., Vol. 49, 1984, pp. 27-59. Zbl0567.35069MR762786
28. [28] H. Tanabe, Equations of evolutions. London: Pitman1979. 
29. [29] S. Ukai, A solution formula for the Stokes equation in Rn+. Comm. Pure Appl. Math., Vol. 40, 1987, pp. 611-621. Zbl0638.76040MR896770
30. [30] W. von WAHL, The equations of Navier-Stokes and abstract parabolic equations. Braunschweig Wiesbaden: Vieweg1985. MR832442