论文标题
用于可压缩流动流的半群良好性 - 不可压缩流体互动PDE系统的INF -SUP方法
An inf-sup approach to semigroup wellposedness for a compressible flow - incompressible fluid interactive PDE system
论文作者
论文摘要
这项工作在部分偏微分方程（PDE）系统上呈现定性和数值结果，该系统对某些流体流体相互作用动力学进行了建模。该系统在域中建模$ω^+ \ subset \ mathbb {r}^2 $中的可压缩流体，并与不可压缩的流体结合，由domain $ω^ - \ subset \ subset \ subbb {r}^2 $模拟的不可压缩的流体，并具有强大的耦合，并在某些方面实现了共享的界面条件，该条件是$ consshene cromence inthere croments interface $ underface $ g。该系统的良好性是通过为其构造半群发电机表示的。通过将其识别为某个边界值问题的解决方案，而良好性是通过babuska-brezzi定理来确定良好性的同时，通过将其识别为某个边界值问题的解决方案来实现这种表示。在后面的部分中，我们演示了较早的良好良好性的建设性证明如何自然地适合某种有限元方法（FEM），从而在数值上近似给定的耦合PDE系统的解决方案。该FEM提供了错误估计和相关的收敛速率。
This work presents qualitative and numerical results on a system of partial differential equations (PDEs) which models certain fluid-fluid interaction dynamics. This system models a compressible fluid in a domain $Ω^+ \subset \mathbb{R}^2$, coupled to an incompressible fluid modeled by Stokes flow in domain $Ω^- \subset \mathbb{R}^2$, with the strong coupling implemented through certain boundary conditions on the shared interface, $Γ$. The wellposedness of this system is established by means of constructing for it a semigroup generator representation. This representation is accomplished by eliminating one of the pressure variables via identifying it as the solution of a certain boundary value problem, while the wellposedness is established via a nonstandard usage of the Babuska-Brezzi Theorem. In later sections, we demonstrate how the earlier constructive proof of wellposedness naturally lends itself to a certain finite element method (FEM), by which to numerically approximate solutions of the given coupled PDE system. This FEM is provided with error estimates and associated rates of convergence.
