SuperDiffusivity in a Shear Flow Modelfrom Perpetual Homogenization
Abstract
This paper is concerned with the asymptotic behavior solutions of stochastic differential equations dy_{t}=dω_{t}∇Γ(y_{t}) dt, y_{0}=0 and d=2. Γ is a 2 &\times 2 skewsymmetric 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 (?[y^{t}^{2}] t^{1+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
 EPrint:
 Communications in Mathematical Physics, 227(2):281302, 2002