@article{AIHPB_2002__38_2_229_0, author = {Giraud, Christophe}, title = {On regular points in {Burgers} turbulence with stable noise initial data}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {229--251}, publisher = {Elsevier}, volume = {38}, number = {2}, year = {2002}, mrnumber = {1899112}, zbl = {0994.35106}, language = {en}, url = {http://www.numdam.org/item/AIHPB_2002__38_2_229_0/} }
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 SP - 229 EP - 251 VL - 38 IS - 2 PB - Elsevier UR - http://www.numdam.org/item/AIHPB_2002__38_2_229_0/ LA - en ID - AIHPB_2002__38_2_229_0 ER -
Giraud, Christophe. On regular points in Burgers turbulence with stable noise initial data. Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) no. 2, pp. 229-251. http://www.numdam.org/item/AIHPB_2002__38_2_229_0/
[1] Statistical properties of shocks in Burgers turbulence, Comm. Math. Phys. 172 (1995) 13-38. | MR | Zbl
, ,[2] Statistical properties of shocks in Burgers turbulence II, Comm. Math. Phys. 169 (1995) 45-59. | MR | Zbl
,[3] Lévy Processes, Cambridge University Press, Cambridge, 1996. | MR | Zbl
,[4] The inviscid Burgers equation with brownian initial velocity, Comm. Math. Phys. 193 (1998) 397-406. | MR | Zbl
,[5] Large deviation estimate in Burgers turbulence with stable noise initial data, J. Stat. Phys. 91 (1998) 655-667. | MR | Zbl
,[6] Structure of shocks in Burgers turbulence with stable noise initial data, Comm. Math. Phys. 203 (1999) 729-741. | MR | Zbl
,[7] The Nonlinear Diffusion Equation, Dordrecht, Reidel, 1974. | Zbl
,[8] On a quasi linear parabolic equation occuring in aerodynamics, Quart. Appl. Math. 9 (1951) 225-236. | MR | Zbl
,[9] Exact statistical properties of the Burgers equation, J. Fluid. Mech. 417 (2000) 69-99. | MR | Zbl
, ,[10] Uniform local behavior of stable subordinators, Ann. Probab. 7 (1979) 1003-1013. | MR | Zbl
,[11] Splitting times and shift functionals, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 47 (1979) 69-81. | MR | Zbl
,[12] Brownian motion with a parabolic drift Airy functions, Probab. Theory Related Fields 81 (1989) 79-109. | MR
,[13] A remark on shocks in inviscid Burgers turbulence, in: , (Eds.), Non-linear Waves Weak Turbulence, Birkhäuser, Boston, 1992, pp. 339-345. | MR | Zbl
,[14] A lower Lipschitz condition for the stable subordinators, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 17 (1971) 23-32. | MR | Zbl
,[15] The partial differential equation ut+uux=μuxx, Comm. Pure Appl. Math. 3 (1950) 201-230. | Zbl
,[16] Hausdorff dimension of regular points in stochastic flows with Lévy α-stable initial data, J. Stat. Phys. 86 (1997) 277-299. | Zbl
, ,[17] Limit Theorems for Random Fields with Singular Spectrum, Math. Appl., Kluwers Academic, 1999. | MR | Zbl
,[18] Large-deviation analysis of Burgers turbulence with white-noise initial data, Comm. Pure Appl. Math. 51 (1998) 47-75. | MR | Zbl
,[19] The inviscid Burgers equation with initial data of Brownian type, Comm. Math. Phys. 148 (1992) 623-641. | MR | Zbl
, , ,[20] Statistics of shocks in solutions of inviscid Burgers equation, Comm. Math. Phys. 148 (1992) 601-621. | MR | Zbl
,[21] Burgers-KPZ Turbulence, Göttingen Lectures, Lectures Notes in Math., 1700, Springer, 1998. | MR | Zbl
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