CaltechAUTHORS
  A Caltech Library Service

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. https://resolver.caltech.edu/CaltechAUTHORS:20160224-110658762

[img] PDF - Submitted Version
See Usage Policy.

282Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20160224-110658762

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s002200200640DOIArticle
https://link.springer.com/article/10.1007%2Fs002200200640PublisherArticle
https://rdcu.be/KJckPublisherFree ReadCube access
http://arxiv.org/abs/math/0105199arXivDiscussion Paper
ORCID:
AuthorORCID
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.
Funders:
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
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:03 Oct 2019 09:40

Repository Staff Only: item control page