论文标题
规律性导致2D流体结构相互作用
Regularity results in 2D fluid-structure interaction
论文作者
论文摘要
我们研究了不可压缩的流体在二维中的相互作用与弹性结构产生物理结构域的运动边界的相互作用。结构的位移由线性粘弹性梁方程描述。我们的主要结果是存在独特的全球强大解决方案。以前，仅考虑平坦参考几何形状的理想情况，以使结构只能沿垂直方向移动。如果结构甚至可以占据完整的边界，我们允许进行一般的几何设置。 我们的主要工具 - 具有独立感兴趣 - 是对边界规律性最小的域中稳定Stokes系统的最大规律性估计。特别是，我们可以根据$ w^{2,2} $在$ l^2 $中的强度属于边界属于$ w^{3/2,2} $的速度。这将应用于移动域中的动量方程（固定时间），材料导数为右侧。由于移动边界仅属于$ w^{2,2} $类的先验性，因此已知结果在这里不适用，因为它们需要$ c^2 $ boundary。
We study the interaction of an incompressible fluid in two dimensions with an elastic structure yielding the moving boundary of the physical domain. The displacement of the structure is described by a linear viscoelastic beam equation. Our main result is the existence of a unique global strong solution. Previously, only the ideal case of a flat reference geometry was considered such that the structure can only move in vertical direction. We allow for a general geometric set-up, were the structure can even occupy the complete boundary. Our main tool -- being of independent interest -- is a maximal regularity estimate for the steady Stokes system in domains with minimal boundary regularity. In particular, we can control the velocity in $W^{2,2}$ in terms of a forcing in $L^2$ provided the boundary belongs roughly to $W^{3/2,2}$. This is applied to the momentum equation in the moving domain (for a fixed time) with the material derivative as right-hand side. Since the moving boundary belongs a priori only to the class $W^{2,2}$, known results do not apply here as they require a $C^2$-boundary.
