论文标题
可压缩的Navier-Stokes-stokes-Stokes-tofor液和阻尼板方程之间相互作用系统的强大解决方案的存在和独特性
Existence and uniqueness of strong solutions for the system of interaction between a compressible Navier-Stokes-Fourier fluid and a damped plate equation
论文作者
论文摘要
该文章致力于流体结构相互作用系统的数学分析，其中流体可压缩和热导通，结构可变形并位于流体结构域边界的一部分上。流体运动是由可压缩的Navier-Stokes-Foury系统建模的，结构位移由结构抑制的板方程描述。我们的主要结果是在$ l^p-l^Q $设置中存在强大解决方案，用于少量时间或小型数据。通过变量的更改和固定点参数，主要结果的证明主要基于相应线性系统的最大规则性属性。在很小的时间内，通过将线性系统解耦为几个标准线性系统，而对于全球存在和较小的数据，可以获得此属性，则通过证明相应的线性耦合{\ em em fluid}操作员是$ \ nathcal {r} - $ pectorial，证明了最大的规则性属性。
The article is devoted to the mathematical analysis of a fluid-structure interaction system where the fluid is compressible and heat conducting and where the structure is deformable and located on a part of the boundary of the fluid domain. The fluid motion is modeled by the compressible Navier-Stokes-Fourier system and the structure displacement is described by a structurally damped plate equation. Our main results are the existence of strong solutions in an $L^p-L^q$ setting for small time or for small data. Through a change of variables and a fixed point argument, the proof of the main results is mainly based on the maximal regularity property of the corresponding linear systems. For small time existence, this property is obtained by decoupling the linear system into several standard linear systems whereas for global existence and for small data, the maximal regularity property is proved by showing that the corresponding linear coupled {\em fluid-structure} operator is $\mathcal{R}-$sectorial.
