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.

中文翻译：

---

3D 中不可压缩粘性流体和热弹性板相互作用问题的弱解

在本文中，我们处理不可压缩粘性流体和非线性热弹性板之间的非线性相互作用问题。板方程中的非线性对应于各种物理相关的半线性和拟线性板模型中的非线性弹性力。我们通过构造一个混合逼近方案来证明这个问题的弱解的存在，该方案通过算子分裂将系统解耦为两个子问题，一个是分段静止的流体，一个是时间连续的有限基为结构。为了证明近似拟线性弹性力的收敛性，我们开发了一种依赖于该非线性函数的最大单调性的补偿紧凑性方法。