On a probabilistic description of small scale structures in 3D fluids

Franco Flandoli

Annales de l'I.H.P. Probabilités et statistiques (2002)

  • Volume: 38, Issue: 2, page 207-228
  • ISSN: 0246-0203

How to cite

top

Flandoli, Franco. "On a probabilistic description of small scale structures in 3D fluids." Annales de l'I.H.P. Probabilités et statistiques 38.2 (2002): 207-228. <http://eudml.org/doc/77714>.

@article{Flandoli2002,
author = {Flandoli, Franco},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {small scale structures; vortex structure; three-dimensional Brownian motion; interaction energy; total energy; intersection local time},
language = {eng},
number = {2},
pages = {207-228},
publisher = {Elsevier},
title = {On a probabilistic description of small scale structures in 3D fluids},
url = {http://eudml.org/doc/77714},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Flandoli, Franco
TI - On a probabilistic description of small scale structures in 3D fluids
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2002
PB - Elsevier
VL - 38
IS - 2
SP - 207
EP - 228
LA - eng
KW - small scale structures; vortex structure; three-dimensional Brownian motion; interaction energy; total energy; intersection local time
UR - http://eudml.org/doc/77714
ER -

References

top
  1. [1] Akao J., Unpublished manuscript, UC Berkeley, 1996; Phase transitions and connectivity in the three-dimensional vortex equilibria, Ph.D Thesis, UC Berkeley, 1994. 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. [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. Zbl0702.76041
  3. [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. Zbl0755.76062MR1174419
  4. [4] E. Bolthausen, On the construction of the three-dimensional polymer measure, Probab. Theory Related Fields97 (1993) 81-101. Zbl0794.60104MR1240717
  5. [5] A. Chorin, Vorticity and Turbulence, Springer, New York, 1994. Zbl0795.76002MR1281384
  6. [6] H. Crauel, F. Flandoli, Attractors for random dynamical systems, Probab. Theory Related Fields100 (1994) 365-393. Zbl0819.58023MR1305587
  7. [7] F. Flandoli, Dissipativity and invariant measures for stochastic Navier–Stokes equations, Nonlin. Diff. Eq. Appl.1 (1994) 403-423. Zbl0820.35108
  8. [8] F. Flandoli, D. Ga̧tarek, Martingale and stationary solutions for stochastic Navier–Stokes equations, Probab. Theory Related Fields102 (1995) 367-391. Zbl0831.60072
  9. [9] F. Flandoli, B. Maslowski, Ergodicity of the 2-D Navier–Stokes equation under random perturbations, Comm. Math. Phys.171 (1995) 119-141. Zbl0845.35080
  10. [10] G. Gallavotti, Meccanica dei Fluidi, Quaderni CNR – GNAFA, 52, Roma, 1996. 
  11. [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. Zbl0822.60048MR1324319
  12. [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. Zbl0554.60066MR876080
  13. [13] N.S. Landkof, Foundations of Modern Potential Theory, Springer, New York, 1972. Zbl0253.31001MR350027
  14. [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. Zbl0563.60072MR889492
  15. [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. Zbl0779.60068MR1229519
  16. [16] P.L. Lions, On Euler Equations and Statistical Physics, Quaderni Scuola Nornale Superiore of Pisa, Pisa, 1997. Zbl1024.35085MR1657480
  17. [17] C. Marchioro, M. Pulvirenti, Mathematical Theory of Incompressible Nonviscous Fluids, Springer, Berlin, 1994. Zbl0789.76002MR1245492
  18. [18] P.L. Lions, A. Majda, Equilibrium statistical theory for nearly parallel vortex filaments, Comm. Pure Appl. Math.53 (2000), to appear. Zbl1041.76038MR1715529
  19. [19] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer, Berlin, 1994. Zbl0804.60001MR1303781
  20. [20] J. Rosen, A local time approach to the self-intersections of Brownian paths in space, Comm. Math. Phys.88 (1983) 327-338. Zbl0534.60070MR701921
  21. [21] J. Rosen, A representation for the intersection local time of Brownian motion in space, Ann. Probab.13 (1985) 145-153. Zbl0561.60086MR770634
  22. [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. Zbl0564.60052MR889483
  23. [23] F. Russo, P. Vallois, The generalized covariation process and Ito formula, Stoch. Proc. Their Appl.59 (1995) 81-104. Zbl0840.60052MR1350257
  24. [24] F. Russo, P. Vallois, Ito formula for C1-functions of semimartinagales, Probab. Theory Relat. Fields104 (1996) 27-41. Zbl0838.60045MR1367665
  25. [25] A.-S. Sznitman, Brownian Motion, Obstacles and Random Media, Springer, Berlin, 1998. Zbl0973.60003MR1717054
  26. [26] B. Toth, W. Werner, The true self-repelling motion, Probab. Theory Related Fields111 (1998) 375-452. Zbl0912.60056MR1640799
  27. [27] M.I. Vishik, A.V. Fursikov, Mathematical Problems of Statistical Hydromechanics, Kluwer, Dordrecht, 1980. Zbl0688.35077MR591678
  28. [28] J. Westwater, On Edwards model for long polymer chains, Comm. Math. Phys.72 (1980) 131-174. Zbl0431.60100MR573702
  29. [29] M. Yor, Compléments aux formules de Tanaka–Rosen, in: Sém. de Prob. XIX, 1983/84, LNM, 1123, Springer, Berlin, 1985, pp. 332-348. Zbl0563.60073
  30. [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. Zbl0569.60075MR889494

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.