Hardy spaces of solenoidal vector fields, with applications to the navier-stokes equations

Kyushu Journal of Mathematics

Volumn 50, Issue 1, 1996, Pages 1-64

  Miyakawa, Tetsuro ^a  

^a KYUSHU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001781565     PISSN: 13406116     EISSN: None     Source Type: Journal    
DOI: 10.2206/kyushujm.50.1     Document Type: Article

References (50)

1. K. I. Babenko. On stationary solutions of the problem of flow past a body of viscous incompressible fluid. Math. USSR-Sb. 20 (1973), 1-25.
2. J. Bergh and J. Löfström. Interpolation Spaces. An Introduction. Springer-Verlag, Berlin-New York, 1976.
3. W. Borchers and T. Miyakawa. L2 decay for the Navier-Stokes flow in halfspaces. Math. Ann. 282 (1988), 139-155.
4. W. Borchers and T. Miyakawa. Algebraic L2 decay for Navier-Stokes flows in exterior domains. Acta Math. 165 (1990), 189-227.
5. W. Borchers and T. Miyakawa. Algebraic L2 decay for Navier-Stokes flows in exterior domains, II. Hiroshima Math. J. 21 (1991), 621-640.
6. W. Borchers and T. Miyakawa. L2 decay for Navier-Stokes flows in unbounded domains, with application to exterior stationary flows. Arch. Rational Mech. Anal. 118 (1992), 273-295.
7. W. Borchers and T. Miyakawa. On stability of exterior stationary Navier-Stokes flows. Acta Math. 174 (1995), 311-382.
8. R. Coifman, P. L. Lions, Y. Meyer and S. Semmes. Compensated compactness and Hardy spaces. J. Math. Pure Appl. 72 (1993), 247-286.
9. R. Coifman and G. Weiss. Extensions of Hardy spaces and their use in analysis. Bull. Amer. Math. Soc. 83 (1977), 569-645.
10. C. Fefferman, N. M. Riviere and Y. Sagher. Interpolation between Hp spaces: the real method. Trans. Amer. Math. Soc. 191 (1974), 75-81.
11. C. Fefferman and E. M. Stein. Hp spaces of several variables. Acta Math. 129 (1972), 137-193.
12. J. Frehse and M. Ruzicka. On the regularity of the stationary Navier-Stokes equations. Ann. Scuola Norm. Sup. Pisa, Serie IV, 21 (1994), 63-95.
13. J. Frehse and M. Ruzicka. Existence of regular solutions to the stationary Navier-Stokes equations. Preprint, University of Bonn, 1993.
14. J. Frehse and M. Ruzicka. Weighted estimates for the stationary Navier-Stokes equations. University of Bonn, 1993.
15. J. Frehse and M. Ruzicka. Regularity for the stationary Navier-Stokes equations in bounded domains. Preprint, ETH Zürich, 1994.
16. G. P. Galdi. On the asymptotic structure of D-solutions to steady Navier-Stokes equations in exterior domains. Mathematical Problems relating to the Navier-Stokes Equation (Series on Adv. Math, for Appl. Sci. 11). ed. G. P. Galdi. World Scientific, Singapore, 1992
17. C. Gerhardt. Stationary solutions of the Navier-Stokes equations in dimension four. Math. Z. 165 (1979), 193-197.
18. M. Giaquinta and G. Modica. Nonlinear systems of the type of the stationary Navier-Stokes system. J. Reine Angew. Math. 330 (1982), 173-214
19. p (0
20. E. Hopf. Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachr. 4 (1951), 213-231.
21. F. John and L. Nirenberg. On functions of bounded mean oscillation. Comm. Pure Appl. Math. 14 (1961), 415-426.
22. R. Kajikiya and T. Miyakawa. On L2 decay of weak solutions of the Navier-Stokes equations in Rn. Math. Z. 192 (1986), 135-148.
23. T. Kato. Strong Lp-solutions of the Navier-Stokes equation in Rm, with applications to weak solutions. Math. Z. 187 (1984), 471-480.
24. H. Kozono and H. Sohr. Density properties of solenoidal vector fields, with applications to the Navier-Stokes equations in exterior domains. J. Math. Soc. Japan 44 (1992), 307-330.
25. H. Kozono and H. Sohr. On stationary Navier-Stokes equations in unbounded domains. Ricerche di Mat. 152 (1993), 69-86.
26. H. Kozono and M. Yamazaki. Navier-Stokes equations in exterior domains. Preprint, Nagoya University, 1994.
27. S. G. Krantz. Fractional integration on Hardy spaces. Studia Math. 73 (1982), 87-94.
28. O. A. Ladyzhenskaya. The Mathematical Theory of Viscous Incompressible Flow. Gordon & Breach, New York, 1969.
29. J. Leray. Étude de diverses équations intégrates nonlinéaires et quelques problèmes que pose 1'hydro dynamique. J. Math. Pures Appl. 12 (1933), 1-82.
30. J. Leray. Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 63 (1934), 193-248.
31. K. Masuda. Weak solutions of the Navier-Stokes equations. Tôhoku Math. J. 36 (1984), 623-646.
32. T. Miyakawa. Remarks on decay properties of exterior stationary Navier-Stokes flows. Proc. Korea-Japan Symp. Partial Differential Equations (Pohang, Korea, 1994). To appear. GARC, Seoul National University, Seoul, Korea, 1995.
33. T. Miyakawa. On uniqueness of steady Navier-Stokes flows in an exterior domain. Adv. Math. Sci. Appl. 5 (1995), 411-420.
34. 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. 199 (1988), 455-478.
35. A. Novotny and M. Padula. Note about decay of solutions of 3D Navier-Stokes equations in an exterior domain. Differential and Integral Equations. To appear.
36. F. K. G. Odqvist. Über die Randwertaufgaben der Hydro dynamik zäher Flüssigkeiten. Math. Z. 32 (1930), 329-375.
37. A. Pazy. Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, Berlin-New York, 1983.
38. G. De Rham. Differentiable Manifolds. Springer-Verlag, Berlin-New York, 1986.
39. M. E. Schonbek. L2 decay for weak solutions of the Navier-Stokes equations. Arch. Rational Mech. Anal. 88 (1985), 209-222.
40. M. E. Schonbek. Large time behavior of solutions to the Navier-Stokes equations. Commun. Partial Differential Equations 11 (1986), 753-763.
41. M. E. Schonbek. Lower bounds of rates of decay for solutions to the Navier-Stokes equations. J. Amer. Math. Soc. 4 (1991), 423-449.
42. E. M. Stein. Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton, 1970.
43. E. M. Stein. Harmonic Analysis. Princeton University Press, Princeton, 1993.
44. E. M. Stein and G. Weiss. Introduction to Fourier Analysis on Euclidean Space. Princeton University Press, Princeton, 1971.
45. M. H. Taibleson and G. Weiss. The molecular characterization of certain Hardy spaces. Asterisque 77 (1980), 67-149.
46. H. Tanabe. Equations of Evolution. Pitman, London-San Francisco, 1979.
47. R. Témam. Navier-Stokes Equations. North-Holland, Amsterdam, 1977.
48. H. Triebel. Theory of Function Spaces. Birkhäuser Verlag, Basel-Boston, 1983
49. H. Triebel. Theory of Function Spaces II. Birkhäuser Verlag, Basel-Boston, 1992.
50. M. Wiegner. Decay results for weak solutions of the Navier-Stokes equations on Rn. J. London Math. Soc. 35 (1987), 303-313.