On a probabilistic description of small scale structures in 3D fluids
Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) no. 2, pp. 207-228. 
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     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},
     pages = {207--228},
     publisher = {Elsevier},
     volume = {38},
     number = {2},
     year = {2002},
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     zbl = {1017.76074},
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     url = {http://archive.numdam.org/item/AIHPB_2002__38_2_207_0/}
}
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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) no. 2, pp. 207-228. http://archive.numdam.org/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[1] Akao J., Unpublished manuscript, UC Berkeley, 1996; Phase transitions and connectivity in the three-dimensional vortex equilibria, Ph.D Thesis, UC Berkeley, 1994.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

[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 | Zbl

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

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

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

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

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

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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

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

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

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

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

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

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

[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 | Zbl

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

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

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

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

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

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

[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

[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 | Zbl