A simple proof of uniqueness of the particle trajectories for solutions of the Navier-Stokes equations

Nonlinearity

Volumn 22, Issue 4, 2009, Pages 735-746

  Dashti, M ^a   Robinson, J C ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67650745353     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/22/4/003     Document Type: Article

References (18)

1. Adams R A 1975 Sobolev Spaces (Pure and Applied Mathematics vol 65) (New York-London: Academic Press)
2. Chemin J-Y and Lerner N 1995 Flot de champs de vecteurs non lipschitziens et équations de Navier-Stokes J. Diff. Eqns 121 314-28
3. Cotter S L, Dashti M, Robinson J C and Stuart A M 2009 Data assimilation problems in fluid mechanics: Bayesian formulation in function space Inverse Probl. Submitted
4. Dashti M and Robinson J C 2009 The uniqueness of Lagrangian trajectories in Navier-Stokes flows Partial Differential Equations Fluid Mechanics ed J C Robinson and J L Rodrigo (Cambridge: Cambridge University Press) at press
5. Foias C, Guillopé C and Temam R 1985 Lagrangian representation of a flow J. Diff. Eqns 57 440-9
6. Fujita H and Kato T 1964 On the Navier-Stokes initial value problem: I Arch. Ration. Mech. Anal. 16 269-315
7. Fujiwara D 1967 Concrete characterization of the domains of fractional powers of some elliptic differential operators of the second order Proc. Japan Acad. 43 82-6
8. Gilbarg D and Trudinger N S 1983 Elliptic Partial Differential Equations of Second Order (Berlin: Springer)
9. Ladyzhenskaya O A 1958 Solution in the large to the boundary-value problem for the Navier-Stokes equations in two-space variables Sov. Phys. Dokl. 123 1128-31
10. Leray J 1933 Etude de diverses équations intégrates non lineaires et de quelques problémes que pose l'hydrodynamique J. Math. Pures Appl. 12 1-82
11. Lions J-L and Magenes E 1972 Non-homogeneous Boundary Value Problems and Applications vol I (New York: Springer)
12. Lions J-L and Prodi G 1959 Un thorme d'existence et unicit dans les quations de Navier-Stokes en dimension 2. (French) C. R. Acad. Sci. Paris 248 3519-21
13. Priestley H A 1997 Introduction to Integration. (New York: Oxford University Press)
14. Robinson J C 2001 Infinite-Dimensional Dynamical Systems (Cambridge Texts in Applied Mathematics) (Cambridge: Cambridge University Press)
15. Robinson J C and Sadowski W 2008 A criterion for uniqueness of Lagrangian trajectories for weak solutions of the 3d Navier-Stokes equations Commun. Math. Phys. submitted
16. Temam R 1995 Navier-Stokes Equations and Nonlinear Functional Analysis (Philadelphia: SIAM)
17. Temam R 1977 Navier-Stokes Equations (Providence, RI: AMS Chelsea Publishing)
18. Zuazua E 2002 Log-Lipschitz regularity and uniqueness of the flow for a field in C. R. Math. Acad. Sci. Paris 335 17-22