论文标题
在外部圆形域上的局部边界分析数据的Navier-Stokes方程的无粘性极限
The inviscid limit of Navier-Stokes equations for locally near boundary analytic data on an exterior circular domain
论文作者
论文摘要
在他们的经典作品[20]中，Caflisch和Sammartino在不可压缩的Navier-Stokes方程中建立了无粘性极限和边界层的扩展，以在半空间上进行分析数据。随后，随后在其综合章节文章[4]中宣布了可以扩展结果以在外部圆形域上包含分析数据，但是文献中似乎缺少证据。外部域的扩展面临的基本困难是，相应的线性半群在分析空间中可能不像半个空间那样具有关承合理[19]。在本文中，我们解决了更大类的初始数据类别的开放问题。该分辨率是由于以下事实，即在涉及边界涡度配方的框架中开发的框架，足以传播仅在边界附近进行分析的溶液，对绿色函数的分析性估计，适用于边界附近的改编的大地坐标以及sobolev均分析的迭代迭代方案。
In their classical work [20], Caflisch and Sammartino established the inviscid limit and boundary layer expansions of vanishing viscosity solutions to the incompressible Navier-Stokes equations for analytic data on a half-space. It was then subsequently announced in their Comptes rendus article [4] that the results can be extended to include analytic data on an exterior circular domain, however the proof appears missing in the literature. The extension to an exterior domain faces a fundamental difficulty that the corresponding linear semigroup may not be contractive in analytic spaces as was the case on the half-space [19]. In this paper, we resolve this open problem for a much larger class of initial data. The resolution is due to the fact that it suffices to propagate solutions that are analytic only near the boundary, following the framework developed in the recent works that involve the boundary vorticity formulation, the analyticity estimates on the Green function, the adapted geodesic coordinates near a boundary, and the Sobolev-analytic iterative scheme.
