Weighted equation approach to decay rate estimates for the Navier-Stokes equations

Nonlinear Analysis, Theory, Methods and Applications

Volumn 37, Issue 6, 1999, Pages 751-789

  Takahashi, Shuji ^a,b  

^a UNIVERSITY OF PADERBORN   (Germany)

^b TOKYO DENKI UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

INCOMPRESSIBLE FLOW; NAVIER STOKES EQUATIONS; NUMERICAL ANALYSIS; THEOREM PROVING;

PARABOLIC DERIVATIVES; WEIGHTED EQUATIONS;

NONLINEAR EQUATIONS;

EID: 0033197430     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00070-4     Document Type: Article

References (24)

1. [1] W. Borchers, T. Miyakawa, On stability of exterior stationary Navier - Stokes flows, Acta Math. 174 (1995) 311-382.
2. [2] R. Farwig, Partial regularity and weighted energy estimates of global weak solutions of the Navier - Stokes system, Proc. Metz Days, Research Notes, Pitman, London (Preprint-Nr. 1769, FB-Math, Univ. Darmstadt), to appear.
3. [3] R. Farwig, H. Sohr, Global estimates in weighted spaces of weak solutions of the Navier - Stokes equations in exterior domains, Arch. Math. (SFB 256, University of Bonn, Preprint no. 424), to appear.
4. [4] A. Friedman, Partial Differential Equations, Robert E. Krieger, New York, 1976.
5. p and regularity of weak solutions of the Navier - Stokes system, J. Differential Equations 62 (1986) 186-212.
6. p estimates for the Cauchy problem with applications to the Navier - Stokes equations in exterior domains, J. Functional Anal. 102 (1991) 72-94.
7. [7] D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1983.
8. [8] J.G. Heywood, The Navier - Stokes equations: on the existence, regularity and decay of solutions, Indiana Univ. Math. J. 29 (1980) 639-681.
9. m, with applications to weak solutions, Math. Z. 187 (1984) 471-480.
10. [10] G.H. Knightly, On a class of global solutions of the Navier - Stokes equations, Arch. Rat. Mech. Anal. 21 (1966) 211-245.
11. n, SIAM J. Anal. 3 (1972) 506-511.
12. [12] G.H. Knightly, Some decay properties of solutions of the Navier - Stokes equations, Lecture Notes in Mathematics, vol. 771, Springer, Berlin, 1980, pp. 287-298.
13. p estimates for the exterior Stokes flow and an application to the non-stationary Navier - Stokes equations, Indiana Univ. Math. J. 41 (1992) 789-808.
14. [14] H. Kozono, T. Ogawa, Global strong solution and its decay properties for the Navier - Stokes equations in three dimensional domains with non-compact boundaries, Math. Z. 216 (1994) 1-30.
15. [15] H. Kozono, H. Sohr, On a new class of generalized solutions for the Stokes equations in exterior domains, Ann. Scuola Norm. Sup. Pisa 19 (1992) 155-181.
16. [16] S.G. Krantz, Fractional integration on Hardy spaces, Studia Math. 73 (1982) 87-94.
17. [17] K. Masuda, On the stability of incompressible viscous fluid motions past objects, J. Math. Soc. Japan 27 (1975) 294-327.
18. [18] T. Miyakawa, Hardy spaces of solenoidal vector fields, with applications to the Navier - Stokes equations, Kyushu J. Math. 50 (1996) 1-64.
19. [19] R. Mizumachi, On the asymptotic behavior of incompressible viscous fluid motions past bodies, J. Math. Soc. Japan 36 (1984) 497-522.
20. [20] J. Serrin, On the interior regularity of weak solutions of the Navier - Stokes equations, Arch. Rat. Mech. Anal. 9 (1962) 187-195.
21. [21] M.E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, NJ, 1970.
22. [22] M. Struwe, On partial regularity results for the Navier - Stokes equations, Comm. Pure Appl. Math. 41 (1988) 437-458.
23. [23] S. Takahashi, On interior regularity criteria for weak solutions of the Navier - Stokes equations, Manuscripta Math. 69 (1990) 237-254.
24. [24] S. Takahashi, On a regularity criterion up to the boundary for weak solutions of the Navier - Stokes equations, Commun. Partial Differential Equations 17 (1992) 261-285 (Erratum, ibid. 19, 1015-1017 (1994)).