A new regularity criterion for the navier-stokes equations in terms of the direction of vorticity

Monatshefte fur Mathematik

Volumn 144, Issue 3, 2005, Pages 251-257

  Zhou, Yong ^a,b  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b EAST CHINA NORMAL UNIVERSITY   (China)

Author keywords

A priori estimates; Navier Stokes equations; Regularity criterion

Indexed keywords

EID: 15544386470     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00605-004-0266-z     Document Type: Article

References (12)

1. Beale JT, Kato T, Majda A (1984) Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Comm Math Phys 94: 61-66
2. n. Chinese Ann Math Ser B 16: 407-412
3. Beirao da Veiga H, Berselli LC (2002) On the regularizing effect of the vorticity direction in incompressible viscous flows. Differential Integral Equations 15: 345-356
4. Constantin P, Fefferman C (1993) Direction of vorticity and the problem of global regularity for the Navier-Stokes equations. Indiana Univ Math J 42: 775-789
5. P and regularity of weak solutions of the Navier-Stokes system. J Differential Equations 62: 186-212
6. Hopf E (1951) Über die Anfangwertaufgaben für die hydromischen Grundgleichungen. Math Nach 4: 213-321
7. Kozono H, Taniuchi Y (2000) Bilinear estimates in BMO and the Navier-Stokes equations. Math Z 235: 173-194
8. Leray J (1933) Étude de divers équations intégrales nonlinearies et de quelques problemes que posent l'hydrodinamique. J Math Pure Appl 12: 1-82
9. Serrin J (1962) On the interior regularity of weak solutions of the Navier-Stokes equations. Arch Rational Mech Anal 9: 187-195
10. von Wahl W (1985) The Equations of Navier-Stokes and Abstract Parabolic Equations. Braunschweig: Vieweg
11. Zhou Y (2002) A new regularity criterion of weak solutions to the Navier-Stokes equations (preprint)
12. Zhou Y (2004) Direction of vorticity and a new regularity criterion for the Navier-Stokes equations. ANZIAM Journal (to appear)