Exponential convergence to the equilibrium for a class of 1D Lagrangian systems with random forcing

Alexandre Boritchev

Published 2016-01-08Version 1

We prove exponential convergence to the stationary measure for a class of 1d Lagrangian systems with random forcing in the space-periodic setting: $\phi_t+\phi_x^2/2=F^{\omega}, x \in S^1 = \mathbb{R}/\mathbb{Z}$. Thus, we solve a conjecture formulated in \cite{GIKP05}. Our result is a consequence (and the natural stochastic PDE counterpart) of the results obtained in \cite{BK13, EKMS00}. It is also the natural analogue of the corresponding generic deterministic result \cite{ISM09}.