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dc.contributor.authorDeng, Y.
dc.contributor.authorZillinger, C.
dc.date.accessioned2020-07-13T07:45:16Z
dc.date.available2020-07-13T07:45:16Z
dc.date.issued2020
dc.identifier.issn0951-7715
dc.identifier.urihttp://hdl.handle.net/20.500.11824/1123
dc.description.abstractWe 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.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectphase mixing, resonances, asymptotic stability, Euler equations, fluidsen_US
dc.titleOn the smallness condition in linear inviscid damping: monotonicity and resonance chainsen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.arxiv1911.02066
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/H2020/669689en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleNonlinearityen_US


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Reconocimiento-NoComercial-CompartirIgual 3.0 España
Except where otherwise noted, this item's license is described as Reconocimiento-NoComercial-CompartirIgual 3.0 España