# American Institute of Mathematical Sciences

doi: 10.3934/dcdsb.2021251
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## Trajectory statistical solutions for the Cahn-Hilliard-Navier-Stokes system with moving contact lines

 School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China

Received  March 2021 Revised  July 2021 Early access October 2021

The objective of this paper is to consider the long-time behavior of solutions for the Cahn-Hilliard-Navier-Stokes system with moving contact lines. As we know, it is very difficult to obtain the uniqueness of an energy solution for this system even in two dimensions caused by the presence of the strong coupling at the boundary. Thus, we first prove the existence of a trajectory attractor for such system, which is a minimal compact trajectory attracting set for the natural translation semigroup defined on the trajectory space. Furthermore, based on the abstract results (trajectory attractor approach) developed in [38], we construct trajectory statistical solutions for the Cahn-Hilliard-Navier-Stokes system with moving contact lines.

Citation: Bo You. Trajectory statistical solutions for the Cahn-Hilliard-Navier-Stokes system with moving contact lines. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021251
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##### References:
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