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

doi:10.1007/s10473-021-0102-8

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

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

Srđan TRIFUNOVIĆ¹, 王亚光²

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. 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/Abstract

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

Srđan TRIFUNOVIĆ, 王亚光. WEAK SOLUTION TO THE INCOMPRESSIBLE VISCOUS FLUID AND A THERMOELASTIC PLATE INTERACTION PROBLEM IN 3D[J]. 数学物理学报(英文版), 2021, 41(1): 19-38.

Srđan TRIFUNOVIĆ, Yaguang WANG. WEAK SOLUTION TO THE INCOMPRESSIBLE VISCOUS FLUID AND A THERMOELASTIC PLATE INTERACTION PROBLEM IN 3D[J]. Acta mathematica scientia,Series B, 2021, 41(1): 19-38.

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

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

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