We discuss a dynamical system approach to a problem of Burgers turbulence. It is shown that there exists a unique stationary distribution for solutions to spatially periodic inviscid random forced Burgers equation in arbitrary dimension. The construction is based on analysis of minimizing orbits for time-dependent random Lagrangians on a d-dimensional torus. We also discuss how dynamical properties of minimizing trajectories lead to quantitative predictions for physically important universal critical exponents.
|Journal||HP Laboratories Technical Report|
|Publication status||Published - 18 Dec 2000|
- Hamilton-jacobi equation
- Random burgers equation
- Uniqueness of global minimizers