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Echo Chains as a Linear Mechanism: Norm Inflation, Modified Exponents and Asymptotics

Deng, Yu; Zillinger, Christian ORCID iD icon 1
1 Karlsruher Institut für Technologie (KIT)


In this article we show that the Euler equations, when linearized around a low frequency perturbation to Couette flow, exhibit norm inflation in Gevrey-type spaces as time tends to infinity. Thus, echo chains are shown to be a (secondary) linear instability mechanism. Furthermore, we develop a more precise analysis of cancellations in the resonance mechanism, which yields a modified exponent in the high frequency regime. This allows us, in addition, to remove a logarithmic constraint on the perturbations present in prior works by Bedrossian, Deng and Masmoudi, and to construct solutions which are initially in a Gevrey class for which the velocity asymptotically converges in Sobolev regularity but diverges in Gevrey regularity.

Verlagsausgabe §
DOI: 10.5445/IR/1000137436
Veröffentlicht am 15.09.2021
DOI: 10.1007/s00205-021-01697-6
Zitationen: 6
Web of Science
Zitationen: 6
Zitationen: 8
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 10.2021
Sprache Englisch
Identifikator ISSN: 0003-9527, 1432-0673
KITopen-ID: 1000137436
Erschienen in Archive for rational mechanics and analysis
Verlag Springer
Band 242
Heft 1
Seiten 643–700
Vorab online veröffentlicht am 30.07.2021
Nachgewiesen in Web of Science
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