Weighted estimates for nonstationary Navier-Stokes equations

Journal of Differential Equations

Volumn 148, Issue 2, 1998, Pages 422-444

  He, Cheng ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0006771318     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1998.3472     Document Type: Article

References (23)

1. Sh. Agmon, Lectures on elliptic boundary value problems, New York, (1965).
2. H. Beirão da Veiga, On the suitable weak solutions to the Navier-Stokes equations in the whole space, J. Math. Pures Appl. 64 (1985), 77-86.
3. H. Beirão da Veiga, Existence and asymptotic behavior for strong solution of the Navier-Stokes equations on the whole space, Indiana Univ. Math. J. 36 (1987), 149-166.
4. p, Arch. Rational Mech. Anal. 45 (1972), 222-240.
5. G. P. Galdi and C. G. Simader, New estimates for the steady-state Stokes problem in exterior domains with applications tot he Navier-Stokes problem, Differential Integral Equations 7, No. 3 (1994), 847-861.
6. p and regularity of weak solutions of the Navier-Stokes system, J. Differential Equations 61 (1986), 186-212.
7. Cheng He, The Cauchy problem for the Navier-Stokes equations, J. Math. Anal. Appl. 209 (1997), 228-242.
8. Cheng He, Existence and regularity of a class of weak solutions to the Navier-Stokes equations, J. Math. Anal. Appl. 210 (1997), 512-530.
9. J. G. Heywood, Open problems in the theory of the Navier-Stokes equations for viscous incompressible flow, in "Lecture Notes in Math.," Vol. 1431, pp. 1-22, Springer-Verlag, New York/Berlin, 1990.
10. 3, J. Funct. Anal. 9 (1972), 296-305.
11. p-solutions of the Navier-Stokes equations in R", with application to weak solutions, Math. Z. 187 (1984), 471-480.
12. T. Kato, Liapunov functions and monotonolity in the Navier-Stokes equation, in "Lecture Notes in Math.," Vol. 1450, pp. 53-64, Springer-Verlag, New York/Berlin, 1989.
13. T. Kato and G. Ponce, Commutator estimates and the Euler and Navier-Stokes equations, Comm. Pure. Appl. Math. 41 (1988), 891-907.
14. 2 decay of weak solutions of the Navier-Stokes equations in R", Math. Z. 192 (1986), 135-148.
15. O. A. Ladyzhenskaya, "The Mathematical Theory of Viscous Incompressible Flow," Gordon & Breach, New York, 1969.
16. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Uralceva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Transl. Math. Monographs, Vol. 23, Providence, 1968.
17. J. Leray, Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math. 63 (1934), 193-248.
18. J. L. Lions, "Quelques méthodes de résolution des problèmes aux limites non linéaires," Dunod, Paris, 1969.
19. 2 decay for weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal. 88 (1985), 209-222.
20. E. M. Stein, "Singular Integrals and Differentiability Properties of Functions," Princeton Univ. Press, Princeton, NJ, 1970.
21. E. M. Stein, Note on singular integrals, Proc. Amer. Math. Soc. 8 (1957), 250-254.
22. R. Temam, "Navier-Stokes Equations," North-Holland, Amsterdam, 1977.
23. M. Wiegner, Decay results for weak solutions of the Navier-Stokes equations on R", J. London Math. Soc. (2) 35 (1987), 303-313.