Communications in Mathematical Physics

, Volume 227, Issue 2, pp 281–302

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 dyt=dωt−∇Γ(yt) dt, y0=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(x1), with h(x1)=∑n=0γnhn(x1/Rn), where hn are smooth functions of period 1, hn(0)=0, γn and Rn grow exponentially fast with n. We can show that yt has an anomalous fast behavior (?[|yt|2]∼t1+ν with ν > 0) and obtain quantitative estimates on the anomaly using and developing the tools of homogenization.

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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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