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. https://resolver.caltech.edu/CaltechAUTHORS:20160224-110658762
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Abstract
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.
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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. | |||||||||||||||
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Subject Keywords: | Differential Equation; Spatial Scale; Asymptotic Behavior; Smooth Function; Flow Model | |||||||||||||||
Issue or Number: | 2 | |||||||||||||||
DOI: | 10.1007/s002200200640 | |||||||||||||||
Record Number: | CaltechAUTHORS:20160224-110658762 | |||||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20160224-110658762 | |||||||||||||||
Official Citation: | Ben Arous, G. & Owhadi, H. Commun. Math. Phys. (2002) 227: 281. https://doi.org/10.1007/s002200200640 | |||||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||||||||
ID Code: | 64735 | |||||||||||||||
Collection: | CaltechAUTHORS | |||||||||||||||
Deposited By: | Ruth Sustaita | |||||||||||||||
Deposited On: | 24 Feb 2016 20:29 | |||||||||||||||
Last Modified: | 10 Nov 2021 23:34 |
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