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Super-diffusivity in a shear flow model from perpetual homogenization

Ben Arous, Gérard and Owhadi, Houman (2002) Super-diffusivity in a shear flow model from perpetual homogenization. Communications in Mathematical Physics, 227 (2). pp. 281-302. ISSN 0010-3616. doi:10.1007/s002200200640.

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This paper is concerned with the asymptotic behavior solutions of stochastic differential equations dy_t =dω_ t −∇Γ(y_t ) dt, y_0=0 and d=2. Γ is a 2 x 2 skew-symmetric matrix associated to a shear flow characterized by an infinite number of spatial scales Γ_(12) = −Γ_(21) = h(x_1), with h(x_1) = ∑_(n =0)^∞γ_n h^n (x_1/R_n ), where h^n are smooth functions of period 1, h^n (0)=0, γ_ n and R_n grow exponentially fast with n. We can show that y_t has an anomalous fast behavior (?[|y_t |^2]∼t^(1+ν) with ν > 0) and obtain quantitative estimates on the anomaly using and developing the tools of homogenization.

Item Type:Article
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Owhadi, Houman0000-0002-5677-1600
Additional Information:© 2002 Springer-Verlag Berlin Heidelberg. Received: 1 June 2001; Accepted: 11 January 2002. The authors would like to thank the referees for useful comments. Part of this work was supported by the Aly Kaufman fellowship.
Funding AgencyGrant Number
Aly Kaufman fellowshipUNSPECIFIED
Subject Keywords:Differential Equation; Spatial Scale; Asymptotic Behavior; Smooth Function; Flow Model
Issue or Number:2
Record Number:CaltechAUTHORS:20160224-110658762
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Official Citation:Ben Arous, G. & Owhadi, H. Commun. Math. Phys. (2002) 227: 281.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:64735
Deposited By: Ruth Sustaita
Deposited On:24 Feb 2016 20:29
Last Modified:10 Nov 2021 23:34

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