论文标题
与Koiter壳相互作用的不可压缩聚合物液
An incompressible polymer fluid interacting with a Koiter shell
论文作者
论文摘要
我们研究了一个相互耦合的介于宏观壳的方程式系统，该系统建模了稀稀的不可压缩聚合物流体，该系统正在发展并与柔性的koiter类型相互作用并相互作用。 The polymer constitutes a solvent-solute mixture where the solvent is modelled on the macroscopic scale by the incompressible Navier-Stokes equation and the solute is modelled on the mesoscopic scale by a Fokker-Planck equation (Kolmogorov forward equation) for the probability density function of the bead-spring polymer chain configuration.该混合物与非线性弹性壳相互作用，该弹性是聚合物流体物理空间结构域的运动边界。我们使用Koiter的经典模型来描述壳的运动，该运动产生了完全非线性的第四阶双曲方程。我们的主要结果是存在对基础系统的薄弱解决方案，直到Koiter Energy退化或灵活的外壳接近自我交流为止。
We study a mutually coupled mesoscopic-macroscopic-shell system of equations modeling a dilute incompressible polymer fluid which is evolving and interacting with a flexible shell of Koiter type. The polymer constitutes a solvent-solute mixture where the solvent is modelled on the macroscopic scale by the incompressible Navier-Stokes equation and the solute is modelled on the mesoscopic scale by a Fokker-Planck equation (Kolmogorov forward equation) for the probability density function of the bead-spring polymer chain configuration. This mixture interacts with a nonlinear elastic shell which serves as a moving boundary of the physical spatial domain of the polymer fluid. We use the classical model by Koiter to describe the shell movement which yields a fully nonlinear fourth order hyperbolic equation. Our main result is the existence of a weak solution to the underlying system which exists until the Koiter energy degenerates or the flexible shell approaches a self-intersection.
