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Echo Chains as a Linear Mechanism: Norm Inflation, Modified Exponents and Asymptotics.
- Source :
-
Archive for Rational Mechanics & Analysis . Oct2021, Vol. 242 Issue 1, p643-700. 58p. - Publication Year :
- 2021
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *COUETTE flow
*GEVREY class
*EXPONENTS
*PRICE inflation
*INFINITY (Mathematics)
Subjects
Details
- Language :
- English
- ISSN :
- 00039527
- Volume :
- 242
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Archive for Rational Mechanics & Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 152014249
- Full Text :
- https://doi.org/10.1007/s00205-021-01697-6