Linear inviscid damping for monotone shear flows

Zillinger, Christian

doi:10.1090/tran/6942

Linear inviscid damping for monotone shear flows
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Trans. Amer. Math. Soc. 369 (2017), 8799-8855 Request permission

Abstract:

In this article, we prove linear stability, scattering and inviscid damping with optimal decay rates for the linearized 2D Euler equations around a large class of strictly monotone shear flows, $(U(y),0)$, in a periodic channel under Sobolev perturbations. Here, we consider the settings of both an infinite periodic channel of period $L$, $\mathbb {T}_{L}\times \mathbb {R}$, as well as a finite periodic channel, $\mathbb {T}_{L} \times [0,1]$, with impermeable walls. The latter setting is shown to not only be technically more challenging, but to exhibit qualitatively different behavior due to boundary effects.

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