### Abstract

This paper is concerned with the asymptotic behavior solutions of stochastic differential equations dy_{t} = dω_{t} - ∇(y_{t})dt, y_{0} = 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 Γ_{12} = - Γ_{21} = 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 (double-struck E sign [|y_{t}t|^{2}] ∼ t ^{1+v} with v > 0) and obtain quantitative estimates on the anomaly using and developing the tools of homogenization.

Original language | English (US) |
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Pages (from-to) | 281-302 |

Number of pages | 22 |

Journal | Communications in Mathematical Physics |

Volume | 227 |

Issue number | 2 |

DOIs | |

State | Published - May 2002 |

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### ASJC Scopus subject areas

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

### Cite this

*Communications in Mathematical Physics*,

*227*(2), 281-302. https://doi.org/10.1007/s002200200640

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

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 227, no. 2, pp. 281-302. https://doi.org/10.1007/s002200200640

}

TY - JOUR

T1 - Super-diffusivity in a shear flow model from perpetual homogenization

AU - Ben Arous, Gérard

AU - Owhadi, Houman

PY - 2002/5

Y1 - 2002/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0036591073&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036591073&partnerID=8YFLogxK

U2 - 10.1007/s002200200640

DO - 10.1007/s002200200640

M3 - Article

AN - SCOPUS:0036591073

VL - 227

SP - 281

EP - 302

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -