Linear inviscid damping for a class of monotone shear flow in Sobolev spaces

Abstract

In this paper, we prove the decay estimates of the velocity and $H^1$ scattering for the 2D linearized Euler equations around a class of monotone shear flow in a finite channel. Our result is consistent with the decay rate predicted by Case in 1960.

56 pages

References in corpus (2)

• Linear inviscid damping for monotone shear flows in a finite periodic channel, boundary effects, blow-up and critical Sobolev regularity
• Infinite superlinear growth of the gradient for the two-dimensional Euler equation

Cited by in corpus (1)

• Enhanced dissipation, hypoellipticity for passive scalar equations with fractional dissipation