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

作　　者：Srdan TRIFUNOVIC Yaguang WANG Srdan TRIFUNOVIC;王亚光(School of Mathematical Sciences,Shanghai Jiao Tong University,Shanghai 200240,China;School of Mathematical Sciences,MOE-LSC and SHL-MAC,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[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

出　　处：《Acta Mathematica Scientia》2021年第1期19-38,共20页数学物理学报（B辑英文版）

基　　金：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 

分 类 号：O357.1[理学—流体力学]