论文标题
在平面域中的stokes和Navier-Stokes问题的渐近极限，带有消失的孔
Asymptotic limit for the Stokes and Navier-Stokes problems in a planar domain with a vanishing hole
论文作者
论文摘要
我们表明，当孔的直径趋向于0时，stokes operator的特征值将其特征孔收敛于整个域中的Stokes操作员的特征值。关于Navier-Stokes方程式，我们证明，当孔缩小到点$ r $的点，溶液中解决方案的涡度收敛到溶液在刺破域中的涡度（即，删除了点$ r $的整个域）。分析的主要成分是对涡度空间的合适分解，在[7]中阐述的形式主义和潜在理论的某些基础知识。
We show that the eigenvalues of the Stokes operator in a domain with a small hole converge to the eigenvalues of the Stokes operator in the whole domain, when the diameter of the hole tends to 0. The convergence of the eigenspaces and the convergence of the Stokes semigroup are also established. Concerning the Navier--Stokes equations, we prove that the vorticity of the solution in the perforated domain converges as the hole shrinks to a point $r$ to the vorticity of the solution in the punctured domain (i.e. the whole domain with the point $r$ removed). The main ingredients of the analysis are a suitable decomposition of the vorticity space, the formalism elaborated in [7] and some basics of potential theory.
