AI 中文总结
本文证明Landau解在旋转自相似类中具有刚性：当旋转参数充分小或大时，解必为Landau解，分别通过紧性论证和角向耗散强制性实现。
AI 中文摘要
Landau解是定常Navier Stokes方程的一族特殊解，对于研究渐近行为和正则性等定常问题具有重要意义。本文证明了当旋转参数$\alpha$充分小或充分大时，Landau解在旋转自相似类中是刚性的。两部分的论证依赖于不同的方法。对于小旋转情形，我们使用紧性论证，并建立了关于任意Landau解线性化的自相似核的分类引理，该方法也可推广到DSS和RDSS情形。对于大旋转情形，强角向耗散在非轴对称分量上产生额外的强制性，迫使解退化为Landau解。
英文摘要
Landau solution is a special family of solutions to the stationary Navier Stokes equations, which is important for the study of stationary problems such as asymptotic behavior and regularity. In this paper we prove that the Landau solution is rigid in rotated self-similar class when rotation parameter $α$ sufficiently small or large. The arguments in the two parts rely on different approaches. For small rotation, we use the compactness argument and establish a classification lemma of the self-similar kernel of the linearization around any Landau solution, this method can also be extended to DSS and RDSS cases. For large rotation, the strong angular dissipation produces additional coercivity on the non-axisymmetric component, which forces the solution to reduce into Landau solution.
