Linear Inviscid Damping and Vorticity Depletion for Shear Flows

Dongyi Wei; Zhifei Zhang; Weiren Zhao

doi:10.1007/s40818-019-0060-9

Linear Inviscid Damping and Vorticity Depletion for Shear Flows

Dongyi Wei, Zhifei Zhang, Weiren Zhao

Mathematics

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

Abstract

In this paper, we prove the linear damping for the 2-D Euler equations around a class of shear flows under the assumption that the linearized operator has no embedding eigenvalues. For the symmetric flows, we obtain the same decay estimate of the velocity as the monotone shear flows. Moreover, we confirm a new dynamical phenomena found by Bouchet and Morita: the depletion of the vorticity at the stationary streamlines, which along with the vorticity mixing leads to the damping for the base flows with stationary streamlines.

Original language	English (US)
Article number	3
Journal	Annals of PDE
Volume	5
Issue number	1
DOIs	https://doi.org/10.1007/s40818-019-0060-9
State	Published - Jun 1 2019

Keywords

Euler equations
Inviscid damping
Rayleigh equation
Shear flow
Vorticity depletion

ASJC Scopus subject areas

Analysis
Mathematical Physics
General Physics and Astronomy
Geometry and Topology
Applied Mathematics

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10.1007/s40818-019-0060-9

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abstract = "In this paper, we prove the linear damping for the 2-D Euler equations around a class of shear flows under the assumption that the linearized operator has no embedding eigenvalues. For the symmetric flows, we obtain the same decay estimate of the velocity as the monotone shear flows. Moreover, we confirm a new dynamical phenomena found by Bouchet and Morita: the depletion of the vorticity at the stationary streamlines, which along with the vorticity mixing leads to the damping for the base flows with stationary streamlines.",

keywords = "Euler equations, Inviscid damping, Rayleigh equation, Shear flow, Vorticity depletion",

author = "Dongyi Wei and Zhifei Zhang and Weiren Zhao",

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AU - Wei, Dongyi

AU - Zhang, Zhifei

AU - Zhao, Weiren

PY - 2019/6/1

Y1 - 2019/6/1

N2 - In this paper, we prove the linear damping for the 2-D Euler equations around a class of shear flows under the assumption that the linearized operator has no embedding eigenvalues. For the symmetric flows, we obtain the same decay estimate of the velocity as the monotone shear flows. Moreover, we confirm a new dynamical phenomena found by Bouchet and Morita: the depletion of the vorticity at the stationary streamlines, which along with the vorticity mixing leads to the damping for the base flows with stationary streamlines.

AB - In this paper, we prove the linear damping for the 2-D Euler equations around a class of shear flows under the assumption that the linearized operator has no embedding eigenvalues. For the symmetric flows, we obtain the same decay estimate of the velocity as the monotone shear flows. Moreover, we confirm a new dynamical phenomena found by Bouchet and Morita: the depletion of the vorticity at the stationary streamlines, which along with the vorticity mixing leads to the damping for the base flows with stationary streamlines.

KW - Euler equations

KW - Inviscid damping

KW - Rayleigh equation

KW - Shear flow

KW - Vorticity depletion

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JF - Annals of PDE

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Linear Inviscid Damping and Vorticity Depletion for Shear Flows

Abstract

Keywords

ASJC Scopus subject areas

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