论文标题
在Navier的动态滑移边界条件下 - 类似Stokes的问题
On the dynamic slip boundary condition for Navier--Stokes-like problems
论文作者
论文摘要
机械问题中边界条件的选择必须反映所考虑的材料与表面的相互作用，尽管假设不滑移条件是避免在分析中避免边界项，并且通常会忽略滑动效应。除了“静态滑移模型”外，它们还无法准确描述，例如在滑动迅速变化的那一刻，壁剪应力和滑动会突然表现出突然的过冲和随后的放松。当这些效果变得显着时，就会发生所谓的动态滑移现象。我们对具有动态滑移边界条件的类似Navier-Stokes的问题进行了数学分析，这需要对Gelfand三胞胎进行适当的概括和相应的功能空间设置。
The choice of the boundary conditions in mechanical problems has to reflect the interaction of the considered material with the surface, despite the assumption of the no-slip condition is preferred to avoid boundary terms in the analysis and slipping effects are usually overlooked. Besides the "static slip models", there are phenomena not accurately described by them, e.g. in the moment when the slip changes rapidly, the wall shear stress and the slip can exhibit a sudden overshoot and subsequent relaxation. When these effects become significant, the so-called dynamic slip phenomenon occurs. We develop a mathematical analysis of Navier-Stokes-like problems with dynamic slip boundary condition, which requires a proper generalisation of the Gelfand triplet and the corresponding function spaces setting.
