| Título: | Surface Stretching for Ornstein Uhlenbeck Velocity Fields |
| Autores: |
Carmona, Rene; Princeton University Grishin, Stanislav; Princeton University Xu, Lin; Princeton University Molchanov, Stanislav; University of North Carolina at Charlotte |
| Fecha: | 1997-01-01 |
| Publicador: | Electronic communications in probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Mathematics Diffusion Processes, Lyapunov Exponent, Stochastic Flows. 60H10, 60H30 |
| Descripción: | The present note deals with large time properties of the Lagrangian trajectories of a turbulent flow in $R^2$ and $R^3$. We assume that the flow is driven by an incompressible time-dependent random velocity field with Gaussian statistics. We also assume that the field is homogeneous in space and stationary and Markovian in time. Such velocity fields can be viewed as (possibly infinite dimensional) Ornstein-Uhlenbeck processes. In d spatial dimensions we established the (strict) positivity of the sum of the largest $d-1$ Lyapunov exponents. As a consequences of this result, we prove the exponential stretching of surface areas (when $d=3$) and of curve lengths (when $d=2$.) This confirms conjectures found in the theory of turbulent flows. |
| Idioma: | Inglés |
1 On the Non-Convexity of the Time Constant in First-Passage Percolation por Kesten, Harry; Cornell University | 6 Simulations and Conjectures for Disconnection Exponents por Puckette, Emily E.; Occidental College,Werner, Wendelin; Université Paris-Sud and IUF |
2 A Proof of a Conjecture of Bobkov and Houdré por Kwapien, S.; Warsaw University,Pycia, M.; Warsaw University,Schachermayer, W.; University of Vienna | 7 Excursions Into a New Duality Relation for Diffusion Processes por Jansons, Kalvis M.; University College London |
3 Moderate Deviations for Martingales with Bounded Jumps por Dembo, Amir; Stanford University | 8 Percolation Beyond $Z^d$, Many Questions And a Few Answers por Benjamini, Itai; Weizmann Institute of Science,Schramm, Oded; Microsoft Research |
4 Bounds for Disconnection Exponents por Werner, Wendelin; Université Paris-Sud and IUF | 9 Transportation Approach to Some Concentration Inequalities in Product Spaces por Dembo, Amir; Stanford University,Zeitouni, Ofer; Technion - Israel Institute of Technology |
5 The Dimension of the Frontier of Planar Brownian Motion por Lawler, Gregory F.; Duke University | 10 Geometric Ergodicity and Hybrid Markov Chains por Roberts, Gareth O.; University of Cambridge,Rosenthal, Jeffrey S.; University of Toronto |