Communications in Mathematical Physics

, Volume 227, Issue 2, pp 281–302 | Cite as

Super-Diffusivity in a Shear Flow Model¶from Perpetual Homogenization

  • Gérard Ben Arous
  • Houman Owhadi


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 &\times; 2 skew-symmetric matrix associated to a shear flow characterized by an infinite number of spatial scales Γ12=−Γ21=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.


Differential Equation Spatial Scale Asymptotic Behavior Smooth Function Flow Model 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Gérard Ben Arous
    • 1
  • Houman Owhadi
    • 2
  1. 1.DMA, EPFL, 1015 Lausanne, Switzerland. E-mail: gerard.benarous@epfl.chCH
  2. 2.William Davidson Faculty (Bloomfield), Technion, 32000 Haifa, Israel. E-mail:

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