dc.contributor.author Deng, Y. dc.contributor.author Zillinger, C. dc.date.accessioned 2020-07-13T07:45:16Z dc.date.available 2020-07-13T07:45:16Z dc.date.issued 2020 dc.identifier.issn 0951-7715 dc.identifier.uri http://hdl.handle.net/20.500.11824/1123 dc.description.abstract We consider the effects of mixing by smooth bilipschitz shear flows in the linearized Euler equations on $\mathbb{T}_{L}\times\mathbb{R}$. Here, we construct a model which is closely related to a small high frequency perturbation around Couette flow, which exhibits linear inviscid damping for $L$ sufficiently small, but for which damping fails if $L$ is large. In particular, similar to the instabiliity results for convex profiles for a shear flow being bilipschitz is not sufficient for linear inviscid damping to hold. Instead of a eigenvalue-based argument the underlying mechanism here is shown to be based on a new cascade of resonances moving to higher and higher frequencies in $y$, which is distinct from the echo mechanism in the nonlinear problem. en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject phase mixing, resonances, asymptotic stability, Euler equations, fluids en_US dc.title On the smallness condition in linear inviscid damping: monotonicity and resonance chains en_US dc.type info:eu-repo/semantics/article en_US dc.identifier.arxiv 1911.02066 dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/669689 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US dc.journal.title Nonlinearity en_US
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