On regularity criteria in terms of pressure for the Navier-Stokes equations in ℝ3

Proceedings of the American Mathematical Society

Volumn 134, Issue 1, 2006, Pages 149-156

  Zhou, Yong ^a  

^a EAST CHINA NORMAL UNIVERSITY   (China)

Author keywords

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

Indexed keywords

EID: 31144437621     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-05-08312-7     Document Type: Article

References (22)

1. H. Beirao da Veiga, On the smoothness of a class of weak solutions to the Navier-Stokes equations. J. Math. Fluid Mech., 2(2000), no. 4, 315-323. MR1814220 (2001m:35250)
2. L.C. Berselli, G.P. Galdi, Regularity criteria involving the pressure for the weak solutions to the Navier-Stokes equations, Proc. Amer. Math. Soc., 130(2002), no. 12, 3585-3595 (electronic). MR1920038 (2003e:35240)
3. L. Caffarelli, R. Kohn, L. Nirenberg, Partial regularity of suitable weak solutions of the Navier-Stokes equations, Comm. Pure Appl. Math., 35(1982), 771-831. MR0673830 (84m:35097)
4. D. Chae, J. Lee, Regularity criterion in terms of pressure for the Navier-Stokes equations, Nonlinear Analysis, 46(2001), 727-735. MR1857154 (2002g:76032)
5. P. Constantin, C. Foias, Navier-Stokes equations, Chicago Lectures in Mathematics series, (1988). MR0972259 (90b:35190)
6. p and regularity of weak solutions of the Navier-Stokes system, J. Differential Equations, 62(1986), 186-212. MR0833416 (87h:35157)
7. E. Hopf, Uber die Anfangswertaufgabe fur die hydrodynamischen Grundgleichungen (German), Math. Nachr., 4(1951), 213-231. MR0050423 (14:327b)
8. 3,∞-solutions of Navier-Stokes equations and backward uniqueness (Russian), Uspekhi Mat. Nauk, 58(2003), no. 2, 3-44. MR1992563 (2004m:35204)
9. m, with applications to weak solutions, Math. Z., 187(1984), 471-480. MR0760047 (86b:35171)
10. H. Kozono, H. Sohr, Regularity criterion on weak solutions to the Navier-Stokes equations, Adv. Differential Equations, 2(1997), 535-554. MR1441855 (97m:35206)
11. H. Kozono, Y. Taniuchi, Bilinear estimates in BMO and the Navier-Stokes equations, Math. Z., 235(2000), 173-194. MR1785078 (2001g:76011)
12. J. Leray, Étude de divers équations intégrales nonlinearies et de quelques problemes que posent lhydrodinamique, J. Math. Pures. Appl., 12(1931), 1-82.
13. K. Masuda, Weak solutions of the Navier-Stokes equations, Tohoku Math. J., 36(1984), 623-646. MR0767409 (86a:35117)
14. M. O'Leary, Pressure conditions for the local regularity of solutions of the Navier-Stokes equations, Electron. J. Differential Equations (12)(1998), 1-9. MR1625358 (99c:35188)
15. V. Scheffer, Partial regularity of solutions to the Navier-Stokes equations, Pacific J. Math., 66(1976), 535-552. MR0454426 (56:12677)
16. J. Serrin, On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 9(1962), 187-195. MR0136885 (25:346)
17. H. Sohr, Zur Regularitatstheorie der instationaren Gleichungen von Navier-Stokes. Math. Z. 184(1983), no. 3, 359-375. MR0716283 (85f:35167)
18. M. Struwe, On partial regularity results for the Navier-Stokes equations, Comm. Pure Appl. Math., 41(1988), 437-458. MR0933230 (89h:35270)
19. R. Temam, Navier-Stokes equations, theory and numerical analysis, AMS Chelsea Publishing (2001). MR1846644 (2002j:76001)
20. G. Tian, Z. Xin, Gradient Estimation on Navier-Stokes equations, Comm. Anal. Geo., 7 (1999), 221-257. MR1685610 (2000i:35166)
21. W. von Wahl, 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, Amer. Math. Soc., Providence, Rhode Island, (1986), 497-503. MR0843635 (87g:35193)
22. Y. Zhou, Regularity criteria in terms of pressure for the 3-D Navier-Stokes equations in a generic domain, Math. Ann., 328(2004), no. 1-2, 173-192. MR2030374 (2004j:35229)