Regularity and stability for the solutions of the Navier-Stokes equations in Lorentz spaces

Nonlinear Analysis, Theory, Methods and Applications

Volumn 35, Issue 6, 1999, Pages 747-764

  Barraza, Oscar A ^a  

^a UNIVERSIDAD NACIONAL DE LA PLATA   (Argentina)

Author keywords

Lorentz spaces; Navier Stokes solution; Navier Stokes system; Partial differential equations; Regularity of solutions; Self similar solution; Stability of solutions; Weak Lp spaces

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; PROBLEM SOLVING; THEOREM PROVING;

LORENTZ SPACES; SELF-SIMILAR SOLUTIONS;

NAVIER STOKES EQUATIONS;

EID: 0033101508     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00027-3     Document Type: Article

References (24)

1. p -spaces of the Navier-Stokes equations Rev. Matem. Iberoam. 12(2):1996;411-439.
2. J. Bergh, J. Löfström, Interpolation Spaces, An Introduction, Springer, Berlin, 1976.
3. M. Cannone, Ondelettes, Paraproduits et Navier-Stokes, Thesis, Université Paris IX-Dauphine, 1994.
4. M. Cannone, Ondelettes, Paraproduits et Navier-Stokes, Diderot, Paris, 1995.
5. 3 , to appear in Comm. in P.D.E.
6. A. Carpio, Asymptotic behavior for the vorticity equations in dimensions two and three, Commun. in P.D.E. 19 (5 & 6) (1994) 827-872.
7. J.A. Carrillo, J. Soler, On the Vlasov-Poisson-Focker-Planck equations with measures in Morrey spaces as initial data, preprint 1994.
8. Fujita H., Kato T. On the Navier-Stokes initial value problem I. Arch. National Mech. Anal. 16:1964;269-315.
9. r -theorem of the Helmholtz decomposition of vector fields J. Fac. Sci. Univ. Tokyo Sec I. 24:1977;685-700.
10. 3 with measures as initial vorticity and Morrey spaces Commun. in P.D.E. 14(5):1989;577-618.
11. r of the Navier-Stokes initial value problems Arch. Rational Mech. Anal. 89:1995;267-281.
12. Giga Y., Miyakawa T., Osada H. Two-dimensional Navier-Stokes flow with measures as initial vorticity. Arch. Rat. Mech. Anal. 104:1988;223-250.
13. R. Hunt, On L(p,q) spaces. L'Enseignement Mathématique, t. 12 (4) (1966) 249-276.
14. m , with applications to weak solutions Math. Zeit. 187:1984;471-480.
15. Kato T. Strong solutions of the Navier-Stokes equations in Morrey spaces. Bol. Soc. Brasil. Mat. (N.S.). 22-2:1992;127-155.
16. Kato T., Fujita H. On the non-stationary Navier-Stokes system. Rend. Sem. Math. Univ. Padova. 32:1962;243-260.
17. 2) Rev. Matem. Iberoamericana. 2:1986;73-88.
18. H. Kozono, M. Yamazaki, Semilinear heat equations and the Navier-Stokes equation with distributions in new function spaces as initial data, Comm. Partial Differential Equations, 19 (5& 6) (1994) 959-1014.
19. n,∞ C. R. Acad. Sci. Paris Sér. I. 320:1995;685-690.
20. n,∞ Houston J. Math. 21:1995;755-799.
21. Leray J. Études de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique. J. Math. Pure Appl. Sér. 912:1933;1-82.
22. O'Neil R. Convolution operators and L(p,q) spaces. Duke Math. J. 30:1963;129-142.
23. Stein E., Weiss G. Introduction to Fourier Analysis on Euclidean Spaces. 1971;Princeton University Press, Princeton.
24. W. von Wahl, The Equations of Navier-Stokes and Abstract Parabolic Equations, Vieweg, Braunschweig, 1985.