Regularity criteria in terms of pressure for the 3-D Navier-stokes equations in a generic domain

Mathematische Annalen

Volumn 328, Issue 1-2, 2004, Pages 173-192

  Zhou, Yong ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

A priori estimates; Integrability of pressure; Navier Stokes equations; Regularity Criterion

Indexed keywords

EID: 0742323551     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00208-003-0478-x     Document Type: Article

References (26)

1. n. Chinese Ann. Math. 16, 407-412 (1995)
2. Beirão da Veiga, H.: Concerning the regularity of the solutions to the Navier-Stokes equations via the trunction method. Part I, Diff. Int. Eqs. 10, 381-391 (1997)
3. Beirao da Veiga, H.: A sufficient condition on the pressure for the regularity of weak solutions to the Navier-Stokes equations. J. Math. Fluid Mech. 2, 99-106 (2000)
4. Beirao da Veiga, H.: Existence and asymptotic behavior for strong solutions of the Navier-Stokes equations in the whole space. Indiana Univ. Math. J. 36(1), 149-166 (1987)
5. Berselli, L.C., Galdi, G.P.: Regularity criteria involving the pressure for the weak solutions to the Navier-Stokes equations. Proc. Amer. Math. Soc. 130(12), 3585-3595 (2002)
6. Caffarelli, L., Kohn, R., Nirenberg, L.: Partial regularity of suitable weak solutions of the Navier-Stokes equations. Comm. Pure Appl. Math. 35, 771-831 (1982)
7. Chae, D., Choe, H-J.: On the regularity criterion for the solutions of the Navier-Stokes equations, Electron. J. Diff. Eqs. 1999 (05), 1-7 (1999)
8. Chae, D., Lee, J.P: Regularity criterion in terms of pressure for the Navier-Stokes equations. Nonlinear Analysis 46, 727-735 (2001)
9. p and regularity of weak solutions of the Navier-Stokes system. J. Diff. Eqs. 62, 186-212 (1986)
10. Hopf, E.: Über die Anfangwertaufgaben für die hydromischen Grundgleichungen. Math. Nach. 4, 213-321 (1951)
11. q spaces. Math. Ann. 285, 265-288 (1989)
12. m, with applications to weak solutions. Math. Z. 187, 471-480 (1984)
13. n. J. Diff. Eqs. 79, 79-88 (1989)
14. Kozono, H., Sohr, H.: Regularity criterion on weak solutions to the Navier-Stokes equations. Adv. Diff. Eqs. 2, 535-554 (1997)
15. Kozono, H., Taniuchi, Y: Bilinear estimates in B M O and the Navier-Stokes equations. Math. Z. 235, 173-194 (2000)
16. Leray, J.: Étude de divers équations intégrales nonlinearies et de quelques problemes que posent lhydrodinamique. J. Math. Pures. Appl. 12, 1-82 (1931)
17. Masuda, K.: Weak solutions of the Navier-Stokes equations. Tohoku Math. J. 36, 623-646 (1984)
18. Scheffer, V.: Partial regularity of solutions to the Navier-Stokes equations. Pacific J. Math. 66, 535-552 (1976)
19. Serrin, J.: On the interior regularity of weak solutions of the Navier-Stokes equations. Arch. Ration. Mech. Anal. 9, 187-195 (1962)
20. Sohr, H.: A regularity class for the Navier-Stokes equations in Lorentz spaces. J. Evolution Eqs. 1, 441-467 (2001)
21. Sohr, H.: A generalization of Serrin's regularity croterion for the Navier-Stokes equations. Quaderni Di Math. (2002), to appear
22. Struwe, M.: On partial regularity results for the Navier-Stokes equations. Comm. Pure Appl. Math 41, 437-458 (1988)
23. Tian, G., Xin, Z.: Gradient Estimation on Navier-Stokes equations. Comm. Anal. Geo. 7, 221-257 (1999)
24. von Wahl, W: Regularity of weak solutions of the Navier-Stokes equations. Proceedings of the 1983 Summer Institute on Nonlinear Functional Analysis and Applications, Proc. Symposia in Pure Mathematics 45, Providence Rhode Island: Amer. Math. Soc., 1989, pp. 497-503
25. 3. Preprint, 2002
26. Zhou, Y: Anew regularity criterion for the Navier-Stokes equations in terms of the gradient of one velocity component. Preprint, 2002