On regular points in Burgers turbulence with stable noise initial data

Christophe Giraud

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

  • Volume: 38, Issue: 2, page 229-251
  • ISSN: 0246-0203

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Giraud, Christophe. "On regular points in Burgers turbulence with stable noise initial data." Annales de l'I.H.P. Probabilités et statistiques 38.2 (2002): 229-251. <http://eudml.org/doc/77715>.

@article{Giraud2002,
author = {Giraud, Christophe},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Burgers turbulence; stable Lévy noise; regular points},
language = {eng},
number = {2},
pages = {229-251},
publisher = {Elsevier},
title = {On regular points in Burgers turbulence with stable noise initial data},
url = {http://eudml.org/doc/77715},
volume = {38},
year = {2002},
}

TY - JOUR
AU - Giraud, Christophe
TI - On regular points in Burgers turbulence with stable noise initial data
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2002
PB - Elsevier
VL - 38
IS - 2
SP - 229
EP - 251
LA - eng
KW - Burgers turbulence; stable Lévy noise; regular points
UR - http://eudml.org/doc/77715
ER -

References

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  1. [1] M. Avellaneda, W. E, Statistical properties of shocks in Burgers turbulence, Comm. Math. Phys.172 (1995) 13-38. Zbl0844.35144MR1346370
  2. [2] M. Avellaneda, Statistical properties of shocks in Burgers turbulence II, Comm. Math. Phys.169 (1995) 45-59. Zbl0857.35143MR1328261
  3. [3] J. Bertoin, Lévy Processes, Cambridge University Press, Cambridge, 1996. Zbl0861.60003MR1406564
  4. [4] J. Bertoin, The inviscid Burgers equation with brownian initial velocity, Comm. Math. Phys.193 (1998) 397-406. Zbl0917.60063MR1618139
  5. [5] J. Bertoin, Large deviation estimate in Burgers turbulence with stable noise initial data, J. Stat. Phys.91 (1998) 655-667. Zbl0927.60039MR1632714
  6. [6] J. Bertoin, Structure of shocks in Burgers turbulence with stable noise initial data, Comm. Math. Phys.203 (1999) 729-741. Zbl0943.60055MR1700933
  7. [7] J.M. Burgers, The Nonlinear Diffusion Equation, Dordrecht, Reidel, 1974. Zbl0302.60048
  8. [8] J.D. Cole, On a quasi linear parabolic equation occuring in aerodynamics, Quart. Appl. Math.9 (1951) 225-236. Zbl0043.09902MR42889
  9. [9] L. Frachebourg, Ph.A. Martin, Exact statistical properties of the Burgers equation, J. Fluid. Mech.417 (2000) 69-99. Zbl0961.76016MR1781884
  10. [10] B.E. Fristedt, Uniform local behavior of stable subordinators, Ann. Probab.7 (1979) 1003-1013. Zbl0438.60060MR548894
  11. [11] R.K. Getoor, Splitting times and shift functionals, Z. Wahrscheinlichkeitstheorie Verw. Gebiete47 (1979) 69-81. Zbl0394.60073MR521533
  12. [12] P. Groeneboom, Brownian motion with a parabolic drift Airy functions, Probab. Theory Related Fields81 (1989) 79-109. MR981568
  13. [13] H. Handa, A remark on shocks in inviscid Burgers turbulence, in: Fitzmaurice, (Eds.), Non-linear Waves Weak Turbulence, Birkhäuser, Boston, 1992, pp. 339-345. Zbl0803.76051MR1276520
  14. [14] J. Hawkes, A lower Lipschitz condition for the stable subordinators, Z. Wahrscheinlichkeitstheorie Verw. Gebiete17 (1971) 23-32. Zbl0193.45002MR282413
  15. [15] E. Hopf, The partial differential equation ut+uux=μuxx, Comm. Pure Appl. Math.3 (1950) 201-230. Zbl0039.10403
  16. [16] A. Janicki, W.A. Woyczynski, Hausdorff dimension of regular points in stochastic flows with Lévy α-stable initial data, J. Stat. Phys.86 (1997) 277-299. Zbl0952.35504
  17. [17] N. Leonenko, Limit Theorems for Random Fields with Singular Spectrum, Math. Appl., Kluwers Academic, 1999. Zbl0963.60048MR1687092
  18. [18] R. Ryan, Large-deviation analysis of Burgers turbulence with white-noise initial data, Comm. Pure Appl. Math.51 (1998) 47-75. Zbl0908.35144MR1486631
  19. [19] Z. She, E. Aurell, U. Frisch, The inviscid Burgers equation with initial data of Brownian type, Comm. Math. Phys.148 (1992) 623-641. Zbl0755.60104MR1181072
  20. [20] Y. Sinai, Statistics of shocks in solutions of inviscid Burgers equation, Comm. Math. Phys.148 (1992) 601-621. Zbl0755.60105MR1181071
  21. [21] W.A. Woyczynski, Burgers-KPZ Turbulence, Göttingen Lectures, Lectures Notes in Math., 1700, Springer, 1998. Zbl0919.60004MR1732301

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