The fractal dimension of the singular set for solutions of the Navier-Stokes system

Nonlinearity

Volumn 22, Issue 12, 2009, Pages 2889-2900

  Kukavica, Igor ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70350652809     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/22/12/005     Document Type: Article

References (21)

1. Constantin P and Foias C 1988 Navier-Stokes Equations (Chicago Lectures in Mathematics) (Chicago, IL: University of Chicago Press)
2. Caffarelli L, Kohn R and Nirenberg L 1982 Partial regularity of suitable weak solutions of the Navier-Stokes equations Commun. Pure Appl. Math. 35 771-831
3. Eden A, Foias C, Nicolaenko B and Temam R 1994 Exponential attractors for dissipative evolution equations RAM: Research in Applied Mathematics vol 37 (Paris: Masson)
4. Falconer K 2003 Fractal Geometry: Mathematical Foundations and Applications 2nd edn (Hoboken, NJ: Wiley)
5. Foias C and Temam R 1979 Some analytic and geometric properties of the solutions of the Navier-Stokes equations J. Math. Pure Appl. 58 339-68
6. Hopf E 1951 ber die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen Math. Nachr. 4 213-31
7. Kukavica I 2008 On partial regularity for the Navier-Stokes equations Discrete Contin. Dyn. Syst. 21 717-28
8. Kukavica I 2008 The partial regularity results for the Navier-Stokes equations Proc. of the Workshop on Partial Differential Equations and Fluid Mechanics (Warwick, UK)
9. Kukavica I 2008 Regularity for the Navier-Stokes equations with a solution in a Morrey space Indiana Univ. Math. J. 57 2843-60
10. Katz N H and Pavlović N 2002 A cheap Caffarelli-Kohn-Nirenberg inequality for the Navier-Stokes equation with hyper-dissipation Geom. Funct. Anal. 12 355-79
11. Lemarié-Rieusset P G 2002 Recent Developments in the Navier-Stokes Problem (Research Notes in Mathematics vol 431) (Boca Raton, FL: Chapman and Hall/CRC Press)
12. Leray J 1934 Sur le mouvement d'un liquide visqueux emplissant l'espace Acta Math. 63 193-248
13. Lin F 1998 A new proof of the Caffarelli-Kohn-Nirenberg theorem Commun. Pure Appl. Math. 51 241-57
14. Ladyzhenskaya O A and Seregin G A 1999 On partial regularity of suitable weak solutions to the three-dimensional Navier-Stokes equations J. Math. Fluid Mech. 1 356-87
15. Robinson J C and Sadowski W 2007 Decay of weak solutions and the singular set of the three-dimensional Navier-Stokes equations Nonlinearity 20 1185-91
16. Robinson J C and Sadowski W 2009 Almost-everywhere uniqueness of Lagrangian trajectories for suitable weak solutions of the three-dimensional Navier-Stokes equations Nonlinearity 22 2093-9
17. Scheffer V 1976 Partial regularity of solutions to the Navier-Stokes equations Pac. J. Math. 66 535-52
18. Scheffer V 1976 Turbulence and Navier-Stokes equations Turbulence and Hausdorff dimension (Lecture Notes in Mathematics vol 565) (Berlin: Springer) pp 174-83 Proc. Conf., Univ. Paris-Sud (Orsay, France, 1975)
19. Scheffer V 1977 Hausdorff measure and the Navier-Stokes equations Commun. Math. Phys. 55 97-112
20. Temam R 2001 Navier-Stokes Equations: Theory and Numerical Analysis (Providence, RI: AMS Chelsea Publishing) (reprint of the 1984 edition)
21. Vasseur A F 2007 A new proof of partial regularity of solutions to Navier-Stokes equations NoDEA Nonlinear Diff. Eqns Appl. 14 753-85