Super-diffusivity in a shear flow model from perpetual homogenization

Gérard Ben Arous, Houman Owhadi

Research output: Contribution to journalArticle

Abstract

This paper is concerned with the asymptotic behavior solutions of stochastic differential equations dyt = dωt - ∇(yt)dt, y0 = 0 and d = 2. Γ is a 2 × 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=0 γnhn (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 (double-struck E sign [|ytt|2] ∼ t 1+v with v > 0) and obtain quantitative estimates on the anomaly using and developing the tools of homogenization.

Original languageEnglish (US)
Pages (from-to)281-302
Number of pages22
JournalCommunications In Mathematical Physics
Volume227
Issue number2
DOIs
StatePublished - May 1 2002

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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