Large time behaviour for a class of turbulence models - stochastic Burgers equations

The aim of this paper is to investigate large time behaviour, i.e. stability and growth bounds, of the solutions for a class of stochastic Burgers equations. The analysis is based on some robustness analysis involved with an infinite-dimensional stochastic evolution equation. Various sufficient conditions for a stochastic Burgers equation are obtained to ensure its asymptotic properties. Lastly, several examples are given to illustrate our theory.