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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

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 &\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.

Keywords

Differential Equation Spatial Scale Asymptotic Behavior Smooth Function Flow Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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: owhadi@techunix.technion.ac.ilIL

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