Trajectory statistical solutions for the Cahn-Hilliard-Navier-Stokes system with moving contact lines

Bo You

doi:10.3934/dcdsb.2021251

Article Contents

2022, Volume 27, Issue 9: 4769-4785. Doi: 10.3934/dcdsb.2021251

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Trajectory statistical solutions for the Cahn-Hilliard-Navier-Stokes system with moving contact lines

Bo You

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

Received: February 28, 2021

Revised: June 30, 2021

Early access: October 2021

Published: September 2022

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Abstract

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.

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Mathematics Subject Classification: 35B41, 35Q35, 76F20.

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