Super-Diffusivity in a Shear Flow Modelfrom Perpetual Homogenization
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=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 (?[|yt|2] t1+ν with ν > 0) and obtain quantitative estimates on the anomaly using and developing the tools of homogenization.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- 2002
- DOI:
- 10.1007/s002200200640
- arXiv:
- arXiv:math/0105199
- Bibcode:
- 2002CMaPh.227..281B
- Keywords:
-
- Mathematics - Probability;
- Mathematical Physics;
- Mathematics - Analysis of PDEs;
- Primary 76F10;
- 76R50;
- secondary 76F30;
- 35B27;
- 34E13;
- 60F05;
- 31C05
- E-Print:
- Communications in Mathematical Physics, 227(2):281--302, 2002