Linear inviscid damping and vorticity depletion for shear flows

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 explicit decay estimates of the velocity, which is the same as one for monotone shear flows. We confirm a new dynamical phenomena found by Bouchet and Morita: the depletion of the vorticity at the stationary streamlines, which could be viewed as a new mechanism leading to the damping for the base flows with stationary streamlines.

arXiv comment76 pages

References in corpus (2)

• On Landau damping
• Large time behavior and asymptotic stability of the two-dimensional Euler and linearized Euler equations

Cited by in corpus (9)

• Transition threshold for the 3D Couette flow in a finite channel
• Inviscid damping near the Couette flow in a channel
• Linear inviscid damping in Gevrey spaces
• Transition threshold for the 3D Couette flow in Sobolev space
• Nonlinear inviscid damping near monotonic shear flows
• Barotropic instability of shear flows
• Stability of the Couette flow at high Reynolds number in 2D and 3D
• Linear inviscid damping near monotone shear flows
• Pseudospectral bound and transition threshold for the 3D Kolmogorov flow