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In a previous article, \cite{Zill3}, we have established linear invisciddamping for a large class of monotone shear flows in a finite periodic channeland have further shown that boundary effects asymptotically lead to theformation of singularities of derivatives of the solution. As the main resultsof this article, we provide a detailed description of the singularity formationand establish stability in all sub-critical fractional Sobolev spaces andblow-up in all super-critical spaces. Furthermore, we discuss the implicationsof the blow-up to the problem of nonlinear inviscid damping in a finiteperiodic channel, where high regularity would be essential to control nonlineareffects.

Linear inviscid damping for monotone shear flows in a finite periodic channel, boundary effects, blow-up and critical Sobolev regularity