Inviscid Damping of Monotone Shear Flows for 2D Inhomogeneous Euler Equation with Non-Constant Density in a Finite Channel

Abstract

We prove the nonlinear inviscid damping for a class of monotone shear flows with non-constant background density for the two-dimensional ideal inhomogeneous fluids in \(\mathbb {T}\times [0,1]\) when the initial perturbation is in Gevrey-\(\frac{1}{s}\) (\(\frac{1}{2}<s<1\)) class with compact support.