数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (1): 19-38.doi: 10.1007/s10473-021-0102-8

• 论文 • 上一篇    下一篇

WEAK SOLUTION TO THE INCOMPRESSIBLE VISCOUS FLUID AND A THERMOELASTIC PLATE INTERACTION PROBLEM IN 3D

Srđan TRIFUNOVIĆ1, 王亚光2   

  1. 1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China;
    2. School of Mathematical Sciences, MOE-LSC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240, China
  • 收稿日期:2020-01-25 出版日期:2021-02-25 发布日期:2021-04-06
  • 通讯作者: Srđan TRIFUNOVIĆ E-mail:sergej1922@gmail.com,tarathis@sjtu.edu.cn
  • 作者简介:Yaguang WANG,E-mail:ygwang@sjtu.edu.cn
  • 基金资助:
    This research was partially supported by National Natural Science Foundation of China (11631008).

WEAK SOLUTION TO THE INCOMPRESSIBLE VISCOUS FLUID AND A THERMOELASTIC PLATE INTERACTION PROBLEM IN 3D

Srđan TRIFUNOVIĆ1, Yaguang WANG2   

  1. 1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China;
    2. School of Mathematical Sciences, MOE-LSC and SHL-MAC, Shanghai Jiao Tong University, Shanghai 200240, China
  • Received:2020-01-25 Online:2021-02-25 Published:2021-04-06
  • Contact: Srđan TRIFUNOVIĆ E-mail:sergej1922@gmail.com,tarathis@sjtu.edu.cn
  • About author:Yaguang WANG,E-mail:ygwang@sjtu.edu.cn
  • Supported by:
    This research was partially supported by National Natural Science Foundation of China (11631008).

摘要: In this paper we deal with a nonlinear interaction problem between an incompressible viscous fluid and a nonlinear thermoelastic plate. The nonlinearity in the plate equation corresponds to nonlinear elastic force in various physically relevant semilinear and quasilinear plate models. We prove the existence of a weak solution for this problem by constructing a hybrid approximation scheme that, via operator splitting, decouples the system into two sub-problems, one piece-wise stationary for the fluid and one time-continuous and in a finite basis for the structure. To prove the convergence of the approximate quasilinear elastic force, we develop a compensated compactness method that relies on the maximal monotonicity property of this nonlinear function.

关键词: fluid-structure interaction, incompressible viscous fluid, nonlinear thermoelastic plate, three space variables, weak solution

Abstract: In this paper we deal with a nonlinear interaction problem between an incompressible viscous fluid and a nonlinear thermoelastic plate. The nonlinearity in the plate equation corresponds to nonlinear elastic force in various physically relevant semilinear and quasilinear plate models. We prove the existence of a weak solution for this problem by constructing a hybrid approximation scheme that, via operator splitting, decouples the system into two sub-problems, one piece-wise stationary for the fluid and one time-continuous and in a finite basis for the structure. To prove the convergence of the approximate quasilinear elastic force, we develop a compensated compactness method that relies on the maximal monotonicity property of this nonlinear function.

Key words: fluid-structure interaction, incompressible viscous fluid, nonlinear thermoelastic plate, three space variables, weak solution

中图分类号: 

  • 35Q30