Inviscid damping of monotone shear flows for 2D inhomogeneous Euler equation with non-constant density

PDE Seminar
Tuesday, September 26, 2023 - 3:30pm for 1 hour (actually 50 minutes)
Wenren Zhao – NYU Abu Dhabi – wz19@nyu.edu
Gong Chen

In this talk, I will discuss my recent research on the asymptotic stability and inviscid damping of 2D monotone shear flows with non-constant density in inhomogeneous ideal fluids within a finite channel. More precisely, I proved that if the initial perturbations belong to the Gevrey-2- class, then linearly stable monotone shear flows in inhomogeneous ideal fluids are also nonlinear asymptotically stable. Furthermore, inviscid damping is proved to hold, meaning that the perturbed velocity converges to a shear flow as time approaches infinity.