The evolution of a random vortex filament

Annals of Probability

Volumn 33, Issue 5, 2005, Pages 1825-1855

  Bessaih, Hakima ^a,c   Gubinelli, Massimiliano ^b,d   Russo, Francesco ^b,d  

^a UNIVERSITY OF WYOMING   (United States)

^b UNIVERSITÉ PARIS 13   (France)

^c UNIVERSITY OF WYOMING   (United States)

^d UNIVERSITÉ PARIS 13   (France)

Author keywords

Path wise stochastic integration; Rough path theory; Vortex filaments

Indexed keywords

EID: 27644440714     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/009117905000000323     Document Type: Article

References (25)

1. BERSELLI, L. C. and BESSAIH, H. (2002). Some results for the line vortex equation. Nonlinearity 15 1729-1746.
2. CHORIN, A. J. (1994). Vorticity and Turbulence. Springer, New York.
3. COUTIN, L. and QIAN, Z. (2002). Stochastic analysis, rough path analysis and fractional Brownian motions. Probab. Theory Related Fields 122 108-140.
4. ERRAMI, M. and Russo, F. (2003). n-covariation, generalized Dirichlet processes and calculus with respect to finite cubic variation processes. Stochastic Process. Appl. 104 259-299.
5. 1,λ-functions of a càdlàg process and related calculus. Probab. Theory Related Fields 122 191-221.
6. FEYEL, D. and DE LA PRADELLE, A. (2004). Curvilinear integrals along rough paths. Preprint.
7. FLANDOLI, F. (2002). On a probabilistic description of small scale structures in 3D fluids. Ann. Inst. H. Poincaré Probab. Statist. 38 207-228.
8. FLANDOLI, F. and GUBINELLI, M. (2002). The Gibbs ensemble of a vortex filament. Probab. Theory Related Fields 122 317-340.
9. FLANDOLI, F. and GUBINELLI, M. (2004). Statistics of a vortex filaments model. Preprint.
10. FLANDOLI, F. and MINELLI, I. (2001). Probabilistic models of vortex filaments. Czechoslovak Math. J. 51 713-731.
11. FÖLLMER, H. (1981). Calcul d'Itô sans probabilités. Seminar on Probability XV. Lecture Notes in Math. 850 143-150. Springer, Berlin.
12. FRISCH, U. (1995). Turbulence. Cambridge Univ. Press.
13. FRIZ, P. K. (2004). Continuity of the Itô map for Hölder rough paths with applications to the support theorem in Hölder norm. Preprint.
14. FRIZ, P. K. and VICTOIR, N. (2005). Approximations of the Brownian rough path with applications to stochastic analysis. Ann. Inst. H. Poincaré Probab. Statist. 41 703-724.
15. GALLAVOTTI, G. (2002). Foundations of Fluid Dynamics. Springer, Berlin.
16. GUBINELLI, M. (2004). Controlling rough paths. J. Funct. Anal. 216 86-140.
17. LIONS, P.-L. and MAJDA, A. (2000). Equilibrium statistical theory for nearly parallel vortex filaments. Comm. Pure Appl. Math. 53 76-142.
18. LYONS, T. J. (1998). Differential equations driven by rough signals. Rev. Mat. Iberoamericana 14 215-310.
19. LYONS, T. J. and LI, X. D. (2004). Smoothness of Itô maps and simulated annealing on path spaces. Preprint.
20. LYONS, T. J. and QIAN, Z. (2002). System Control and Rough Paths. Oxford Univ. Press.
21. MOORE, D. W. (1972). Finite amplitude waves on aircraft trailing vortices. Aero. Quarterly 23 307-314.
22. NUALART, D., ROVIRA, C. and TINDEL, S. (2003). Probabilistic models for vortex filaments based on fractional Brownian motion. Ann. Probab. 31 1862-1899.
23. ROSENHEAD, L. (1930). The spread of vorticity in the wake behind a cylinder. Proc. Roy. Soc. London Ser. A 127 590-612.
24. RUSSO, F. and VALLOIS, P. (1995). The generalized covariation process and Itô formula. Stochastic Process. Appl. 59 81-104.
25. YOUNG, L. C. (1936). An inequality of Hölder type, connected with Stieltjes integration. Acta Math. 67 251-282.