Abstract
We prove a local regularity result for the non-stationary three-dimensional Navier-Stokes equations. Bibliography: 10 titles.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Takahashi, “On interior regularity criteria for weak solutions of the Navier-Stokes equations,” Manuscripta Math., 69, 237–254 (1990).
Z.-M. Chen and W. G. Price, “Blow-up rate estimates for weak solutions of the Navier-Stokes equations,” R. Soc. Lond. Proc., Ser. A, Math. Phys. Eng. Sci., 457, 2625–2642 (2001).
H. Kim and H. Kozono, “Interior regularity criteria in weak spaces for the Navier-Stokes equations,” Manuscripta Math., 115, 85–100 (2004).
J. Serrin, “On the interior regularity of weak solutions of the Navier-Stokes equations,” Arch. Rat. Mech. Anal., 9, 187–195 (1962).
M. Struwe, “On partial regularity results for the Navier-Stokes equations,” Comm. Pure Appl. Math., 41, 437–458 (1988).
F.-H. Lin, “A new proof of the Caffarelly-Kohn-Nirenberg theorem,” Comm. Pure Appl. Math., 51, 241–257 (1998).
L. Caffarelli, R.-V. Kohn, and L. Nirenberg, “Partial regularity of suitable weak solutions of the Navier-Stokes equations,” Comm. Pure Appl. Math., XXXV, 771–831 (1982).
G. A. Seregin, “On the number of singular points of weak solutions to the Navier-Stokes equations,” Comm. Pure Appl. Math., 54, 1019–1028 (2001).
O. A. Ladyzhenskaya and G. A. Seregin, “On partial regularity of suitable weak solutions to the threedimensional Navier-Stokes equations,” J. Math. Fluid Mech., 1, 356–387 (1999).
L. Escauriaza, G. Seregin, and V. Šverák, “L 3,∞-Solutions to the Navier-Stokes equations and backward uniqueness,” Usp. Mat. Nauk, 58, 2(350), 3–44 (2003).
Author information
Authors and Affiliations
Additional information
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 336, 2005, pp. 46–54.
Rights and permissions
About this article
Cite this article
Zajaczkowski, W., Seregin, G.A. Sufficient condition of local regularity for the Navier-Stokes equations. J Math Sci 143, 2869–2874 (2007). https://doi.org/10.1007/s10958-007-0172-8
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10958-007-0172-8