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 2002

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Shear Flow
Diffusivity
homogenizing
shear flow
Homogenization
diffusivity
Skew symmetric matrix
Asymptotic Behavior of Solutions
Smooth function
Anomalous
Anomaly
Stochastic Equations
differential equations
anomalies
Differential equation
estimates
matrices
Model
Estimate

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Super-diffusivity in a shear flow model from perpetual homogenization. / Ben Arous, Gérard; Owhadi, Houman.

In: Communications in Mathematical Physics, Vol. 227, No. 2, 05.2002, p. 281-302.

Research output: Contribution to journalArticle

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