Regularity conditions for the 3D Navier-Stokes equations
Authors:
Jishan Fan and Hongjun Gao
Journal:
Quart. Appl. Math. 67 (2009), 195-199
MSC (2000):
Primary 35Q30; Secondary 76D05
DOI:
https://doi.org/10.1090/S0033-569X-09-01119-7
Published electronically:
January 8, 2009
MathSciNet review:
2497603
Full-text PDF Free Access
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Additional Information
Abstract: We obtain logarithmic improvements for conditions of regularity in the 3D Navier-Stokes equations.
References
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References
- J. Leray, Essai sur le mouvement d’un fluide visqueux emplissant l’espace, Acta. Math. 63 (1934), pp. 193-248. MR 1555394
- P. Constantin and C. Foias, Navier-Stokes equations, University of Chicago Press, Chicago, 1988. MR 972259 (90b:35190)
- R. Temam, Navier-Stokes Equations, $3^{rd}$ edn. North Holland, (1984). MR 769654 (86m:76003)
- G. Prodi, Un Teorema di Uniciá per le Equazionni di Navier-Stokes, Ann. Mat. Pura Appl., 48, no. 4 (1959), pp. 173-182. MR 0126088 (23:A3384)
- J. Serrin, On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Rat. Mech. Anal., 9 (1962), pp. 187-191. MR 0136885 (25:346)
- E. Fabes, B. Jones and N. Riviere, The initial value problem for the Navier-Stokes equations with data in $L^p$, Arch. Rat, Mech. Anal., 45 (1972), pp. 222-248. MR 0316915 (47:5463)
- H. Kozono and Y. Taniuchi, Bilinear Estimates in BMO and Navier-Stokes Equations, Math. Z, 235, no. 1 (2000), pp. 173-194. MR 1785078 (2001g:76011)
- L. Escauriaza, G. Seregin and V. Sverak, $L^{3,\infty }$-solutions of Navier-Stokes Equations and Backward Uniqueness, Russian Math. Surveys, 58, no. 2 (2003), pp. 211-250. MR 1992563 (2004m:35204)
- H. Beirão da Veiga, A new regularity class for the Navier-Stokes equations in $\mathbb {R}^n$, Chinese Ann. Math. 16 (1995), 407-412. MR 1380578 (96m:35035)
- S. Montgomery-Smith, Conditions implying regularity of the three dimensional Navier-Stokes equation, Applications of Mathematics, 50 (2005), 451-464. MR 2160072 (2006c:35220)
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Additional Information
Jishan Fan
Affiliation:
Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, People’s Republic of China;
School of Mathematics and Computer Sciences, Nanjing Normal University, Nanjing, 210097, People’s Republic of China
Email:
fanjishan@njfu.com.cn
Hongjun Gao
Affiliation:
School of Mathematics and Computer Sciences, Nanjing Normal University, Nanjing, 210097, People’s Republic of China
Email:
gaohj@hotmail.com
Keywords:
Navier-Stokes equations,
vorticity,
regularity condition.
Received by editor(s):
September 18, 2007
Published electronically:
January 8, 2009
Additional Notes:
The first author was supported by NSFC Grant No. 10301014.
The second author was supported by NSFC Grant (No. 10571087, No. 10871097), SRFDP No. 20050319001, NSF of Jiangsu Province BK2006523, NSF of Jiangsu Education Commission No. 05KJB110063 and the Teaching and Research Award Program for Outstanding Young Teachers in Nanjing Normal University (2005–2008).
Dr. Hongjun Gao is the corresponding author.
Article copyright:
© Copyright 2009
Brown University
The copyright for this article reverts to public domain 28 years after publication.
