The HADES seminar on Tuesday, **May 11 **will be given by **Wenjie Lu** via **Zoom **from **3:40 to 5 pm.**

**Speaker: **Wenjie Lu (University of Minnesota)

**Abstract:** Hydrodynamic stability is one of the oldest problems studied in PDEs. In this talk, I will introduce results related to the linear stability of monotone shear flows with boundaries. If the vorticity vanishes near boundaries, one can obtain optimal decay estimates in Gevery spaces. However, the boundary effect is significant and can be an obstruction for the scattering of the vorticity in high regularity spaces. In order to understand the asymptotic behavior more clearly, we need to have a full picture of the singularity structure of the generalized eigenfunctions. It turns out that we can actually track singularities of arbitrary derivatives of the generalized eigenfunctions. With this, we can get arbitrary many terms in the asymptotic, not only the main term. This is a recent joint work with Hao Jia.