Constructing dynamical global-in-time solutions to 3D incompressible Euler equation is in general challenging. Recently Guo-Pausader-Widmayer made a breakthrough in this direction by proving asymptotic stability of a uniform-rotating static solution. Their approach heavily depends on the “uniform-rotating” of the background solution. In this talk I will present some recent progress on asymptotic linear stability of a more general columnar flow with non-uniform rotation. This is a joint work with Siqi Ren and Zhifei Zhang.