We proved that there exists a unique invariant measure for solutions of stochastic conservation laws with Dirichlet boundary condition driven by multiplicative noise. Moreover, a polynomial mixing property is established. This is done in the setting of kinetic solutions taking values in an L-1-weighted space. 

　　Publication: 

　　Communications in Mathematical Physics (2023) 

　　DOI: 10.1007/s00220-022-04629-x 

　　Author: 

　　Dong Zhao 

　　RCSDS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China. 

　　E-mail: dzhao@amt.ac.cn 

　　Rangrang Zhang 

　　School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China. 

　　Tusheng Zhang 

　　School of Mathematics, University of Science and Technology of China, Hefei 230026, China.