Remarks on the blow-up criterion of the three-dimensional Euler equations

Nonlinearity

Volumn 18, Issue 3, 2005, Pages 1021-1029

  Chae, Dongho ^a  

^a Sungkyunkwan University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 29744469610     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/18/3/005     Document Type: Article

References (25)

1. Beale J T, Kato T and Majda A1984 Remarks on the breakdown of smooth solutions for the 3-D Euler equations Commun. Math. Phys. 94 61-6
2. Chae D 2002 On the well-posedness of the Euler equations in the Besov and the Triebel-Lizorkin spaces Proc. Conf. on Tosio Kato's Method and Principle for Evolution Equations in Mathematical Physics (June 27-29) (Tokyo) pp 42-57
3. Chae D 2002 On the well-posedness of the Euler equations in the Triebel-Lizorkin spaces Commun. Pure Appl. Math. 55 654-78
4. Chae D and Choe H J 1999 Regularity of solutions to the Navier-Stokes equation Electron. J. Dig. Eqns no 5 1-7 (electronic)
5. Chae D and Imanuvilov O 1999 Generic solvability of the axisymmetric 3-D Euler equations and the 2-D Boussinesq equations J. Diff. Eqns 156 1-17
6. Chae D and Kim N 1996 On the breakdown of axisymmetric smooth solutions for the 3-D Euler equations Commun. Math. Phys. 178 391-8
7. Chae D and Lee J 2002 On the regularity of axisymmetric solutions of the Navier-Stokes equations Math. Z. 239 645-71
8. Chemin J Y 1992 Régularité des trajectoires des particules d'un fluide incompressible remplissant l'espace J. Math. Pure Appl. 71407-17
9. Constantin P 1994 Geometric statistics in turbulence SIAM Rev. 36 73-98
10. Constantin P and Fefferman C 1994 Direction of vorticity and the problem of global regularity for the Navier-Stokes equations Indiana Univ. Math. J. 42 775-89
11. Constantin P, Fefferman C and Majda A 1996 Geometric constraints on potential singularity formulation in the 3-D Euler equations Commun. P.D.E. 21 559-71
12. Grauer R and Sideris T 1991 Numerical computation of three dimensional incompressible ideal fluids with swirl Phys. Rev. Lett. 67 3511-14
13. Jawerth B 1977 Some observations on Besov and Lizorkin-Triebel spaces Math. Scand. 40 94-104
14. 3 J. Funct. Anal. 9 296-305
15. Kato T 2001 Untitled manuscript Proc. Conf. on Tosio Kato's Method and Principle for Evolution Equations in Mathematical Physics (June 27-29) (Tokyo) pp 261-70
16. 2) Riv. Math. Ibero-Americana 2 73-88
17. Kerr R 1993 Evidence for a singularity of the 3-dimensional, incompressible Euler equations Phys. Fluids A 5 1725-46
18. Kim N 2001 Remarks on the blow-up of solutions for the 3-D Euler equations Differ. Integral Eqns 14 129-40
19. Kozono H and Taniuchi Y 2000 Limiting case of the Sobolev inequality in BMO, with applications to the Euler equations Commun. Math. Phys. 214 191-200
20. Kozono H, Ogawa T and Taniuchi Y 2002 The critical Sobolev inequalities in Besov spaces and regularity criterion to some semilinear evolution equations Math. Z. 242 251-78
21. Majda A 1986 Vorticity and the mathematical theory of incompressible fluid flow Commun. Pure Appl. Math. 39 187-220
22. Majda A and Bertozzi 2002 Vorticity and Incompressible Flow (Cambridge: Cambridge University Press)
23. s type Z Anal. Anwendungen 14 105-40
24. Stein E M 1970 Singular Integrals and Differentiability Properties of Functions (Princeton, NJ: Princeton University Press)
25. Triebel H 1983 Theory of Function Spaces (Basel: Birkhäuser)