Acta mathematica scientia,Series B ›› 2025, Vol. 45 ›› Issue (6): 2305-2329.doi: 10.1007/s10473-025-0601-0

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GLOBAL STRONG SOLUTIONS TO NAVIER-STOKES/CAHN-HILLIARD EQUATIONS WITH GENERALIZED NAVIER BOUNDARY CONDITION AND DYNAMIC BOUNDARY CONDITION

Shijin DING1, Yinghua LI1, Yuanxiang YAN2,*   

  1. 1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China;
    2. School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510655, China
  • Received:2024-09-27 Revised:2025-04-08 Online:2025-11-25 Published:2025-11-14
  • Contact: *Yuanxiang YAN, E-mail: yuanxiangyan@m.scnu.edu.cn
  • About author:Shijin DING, E-mail: dingsj@scnu.edu.cn; Yinghua LI, E-mail: yinghua@scnu.edu.cn
  • Supported by:
    Ding's research was supported by the Key Project of the NSFC (12131010) and the NSFC (12271032); Li's work was supported by the NSFC (12371205) and the NSF of Guangdong Province (2025A1515012026); Yan's work was supported by the NSF of Guangdong Province (2024A1515013238).

Abstract: In this paper, we consider incompressible Navier-Stokes/Cahn-Hilliard system with the generalized Navier boundary condition and the dynamic boundary condition in a channel, which can describe the interaction between a binary material and the walls of the physical domain. We prove the global-in-time existence and uniqueness of strong solutions to this initial boundary value problem in a 2D channel domain.

Key words: Navier-Stokes/Cahn-Hilliard equations, generalized Navier boundary condition, dynamic boundary condition, existence, uniqueness

CLC Number: 

  • 35A01
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