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arXiv · 1605.05959

On circular flows: linear stability and damping

Christian Zillinger
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Abstract

In this article we establish linear inviscid damping with optimal decay rates around 2D Taylor-Couette flow and similar monotone flows in an annular domain $B_{r_{2}}(0) \setminus B_{r_{1}}(0) \subset \mathbb{R}^{2}$. Following recent results by Wei, Zhang and Zhao, we establish stability in weighted norms, which allow for a singularity formation at the boundary, and additional provide a description of the blow-up behavior.

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Christian Zillinger. 2016-05-19. On circular flows: linear stability and damping. https://arxiv.org/abs/1605.05959

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