On a probabilistic description of small scale structures in 3D fluids
Flandoli, Franco
Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002), p. 207-228 / Harvested from Numdam
@article{AIHPB_2002__38_2_207_0,
     author = {Flandoli, Franco},
     title = {On a probabilistic description of small scale structures in 3D fluids},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {38},
     year = {2002},
     pages = {207-228},
     mrnumber = {1899111},
     zbl = {1017.76074},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2002__38_2_207_0}
}
Flandoli, Franco. On a probabilistic description of small scale structures in 3D fluids. Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) pp. 207-228. http://gdmltest.u-ga.fr/item/AIHPB_2002__38_2_207_0/

[1] Akao J., Unpublished manuscript, UC Berkeley, 1996; Phase transitions and connectivity in the three-dimensional vortex equilibria, Ph.D Thesis, UC Berkeley, 1994.

[2] S. Albeverio, A.B. Cruzeiro, Global flows with invariant (Gibbs) measures for Euler and Navier-Stokes two-dimensional fluids, Comm. Math. Phys. 129 (1990) 431-444. | Zbl 0702.76041

[3] J. Bell, D. Marcus, Vorticity intensification and the transition to turbulence in the three-dimensional Euler equations, Comm. Math. Phys. 147 (1992) 371-394. | MR 1174419 | Zbl 0755.76062

[4] E. Bolthausen, On the construction of the three-dimensional polymer measure, Probab. Theory Related Fields 97 (1993) 81-101. | MR 1240717 | Zbl 0794.60104

[5] A. Chorin, Vorticity and Turbulence, Springer, New York, 1994. | MR 1281384 | Zbl 0795.76002

[6] H. Crauel, F. Flandoli, Attractors for random dynamical systems, Probab. Theory Related Fields 100 (1994) 365-393. | MR 1305587 | Zbl 0819.58023

[7] F. Flandoli, Dissipativity and invariant measures for stochastic Navier-Stokes equations, Nonlin. Diff. Eq. Appl. 1 (1994) 403-423. | Zbl 0820.35108

[8] F. Flandoli, D. Ga̧Tarek, Martingale and stationary solutions for stochastic Navier-Stokes equations, Probab. Theory Related Fields 102 (1995) 367-391. | Zbl 0831.60072

[9] F. Flandoli, B. Maslowski, Ergodicity of the 2-D Navier-Stokes equation under random perturbations, Comm. Math. Phys. 171 (1995) 119-141. | Zbl 0845.35080

[10] G. Gallavotti, Meccanica dei Fluidi, Quaderni CNR - GNAFA, 52, Roma, 1996.

[11] P. Imkeller, V. Perez-Abreu, J. Vives, Chaos expansions of double intersection local time of Brownian motion in Rd and renormalization, Stoch. Proc. Their Appl. 56 (1995) 1-34. | MR 1324319 | Zbl 0822.60048

[12] H. Kunita, Stochastic differential equations and stochastic flows of diffeomorphisms, in: Hennequin P.L. (Ed.), École d'été de Saint-Flour XII, 1982, LNM, 1097, Springer, Berlin, 1984. | MR 876080 | Zbl 0554.60066

[13] N.S. Landkof, Foundations of Modern Potential Theory, Springer, New York, 1972. | MR 350027 | Zbl 0253.31001

[14] J.F. Le Gall, Sur le temps local d'intersection du mouvement Brownien plan, et la méthode de renormalisation de Varadhan, in: Sém. de Prob. XIX 1983/84, LNM, 1123, Springer, Berlin, 1985, pp. 314-331. | Numdam | MR 889492 | Zbl 0563.60072

[15] J.F. Le Gall, Some properties of planar Brownian motion, in: École d'été de Saint-Flour XX, 1990, LNM, 1527, Springer, Berlin, 1992. | MR 1229519 | Zbl 0779.60068

[16] P.L. Lions, On Euler Equations and Statistical Physics, Quaderni Scuola Nornale Superiore of Pisa, Pisa, 1997. | MR 1657480 | Zbl 1024.35085

[17] C. Marchioro, M. Pulvirenti, Mathematical Theory of Incompressible Nonviscous Fluids, Springer, Berlin, 1994. | MR 1245492 | Zbl 0789.76002

[18] P.L. Lions, A. Majda, Equilibrium statistical theory for nearly parallel vortex filaments, Comm. Pure Appl. Math. 53 (2000), to appear. | MR 1715529 | Zbl 1041.76038

[19] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, 1994. | MR 1303781 | Zbl 0804.60001

[20] J. Rosen, A local time approach to the self-intersections of Brownian paths in space, Comm. Math. Phys. 88 (1983) 327-338. | MR 701921 | Zbl 0534.60070

[21] J. Rosen, A representation for the intersection local time of Brownian motion in space, Ann. Probab. 13 (1985) 145-153. | MR 770634 | Zbl 0561.60086

[22] J. Ruiz De Chavez, Sur les integrales stochastiques multiples, in: Sém. de Prob. XIX, 1983/84, LNM, 1123, Springer, Berlin, 1985, pp. 248-262. | Numdam | MR 889483 | Zbl 0564.60052

[23] F. Russo, P. Vallois, The generalized covariation process and Ito formula, Stoch. Proc. Their Appl. 59 (1995) 81-104. | MR 1350257 | Zbl 0840.60052

[24] F. Russo, P. Vallois, Ito formula for C1-functions of semimartinagales, Probab. Theory Relat. Fields 104 (1996) 27-41. | MR 1367665 | Zbl 0838.60045

[25] A.-S. Sznitman, Brownian Motion, Obstacles and Random Media, Springer, Berlin, 1998. | MR 1717054 | Zbl 0973.60003

[26] B. Toth, W. Werner, The true self-repelling motion, Probab. Theory Related Fields 111 (1998) 375-452. | MR 1640799 | Zbl 0912.60056

[27] M.I. Vishik, A.V. Fursikov, Mathematical Problems of Statistical Hydromechanics, Kluwer, Dordrecht, 1980. | MR 591678 | Zbl 0688.35077

[28] J. Westwater, On Edwards model for long polymer chains, Comm. Math. Phys. 72 (1980) 131-174. | MR 573702 | Zbl 0431.60100

[29] M. Yor, Compléments aux formules de Tanaka-Rosen, in: Sém. de Prob. XIX, 1983/84, LNM, 1123, Springer, Berlin, 1985, pp. 332-348. | Numdam | Zbl 0563.60073

[30] M. Yor, Renormalisation et convergence en loi pour le temps locaux d'intersection du mouvement brownien dans R3, in: Sém. de Prob. XIX, 1983/84, LNM, 1123, Springer, Berlin, 1985, pp. 350-365. | Numdam | MR 889494 | Zbl 0569.60075