Nonlinear inviscid damping for a class of monotone shear flows in a finite channel

Nader Masmoudi; Weiren Zhao

doi:10.4007/ANNALS.2024.199.3.3

Nonlinear inviscid damping for a class of monotone shear flows in a finite channel

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the nonlinear inviscid damping for a class of monotone shear flows in T×[0, 1] for initial perturbation in Gevrey- 1/s class (1 < 1/s < 2) with compact support. The main new idea of the proof is to construct and use the wave operator of a slightly modified Rayleigh operator in a well-chosen coordinate system.

Original language	English (US)
Pages (from-to)	1093-1175
Number of pages	83
Journal	Annals of Mathematics
Volume	199
Issue number	3
DOIs	https://doi.org/10.4007/ANNALS.2024.199.3.3
State	Published - 2024

Keywords

Euler equation
inviscid damping
shear flow
wave operator

ASJC Scopus subject areas

Mathematics (miscellaneous)

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10.4007/ANNALS.2024.199.3.3

Cite this

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abstract = "We prove the nonlinear inviscid damping for a class of monotone shear flows in T×[0, 1] for initial perturbation in Gevrey- 1/s class (1 < 1/s < 2) with compact support. The main new idea of the proof is to construct and use the wave operator of a slightly modified Rayleigh operator in a well-chosen coordinate system.",

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AB - We prove the nonlinear inviscid damping for a class of monotone shear flows in T×[0, 1] for initial perturbation in Gevrey- 1/s class (1 < 1/s < 2) with compact support. The main new idea of the proof is to construct and use the wave operator of a slightly modified Rayleigh operator in a well-chosen coordinate system.

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KW - inviscid damping

KW - shear flow

KW - wave operator

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Nonlinear inviscid damping for a class of monotone shear flows in a finite channel

Abstract

Keywords

ASJC Scopus subject areas

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