Abstract: In this talk, I will talk about the vortex solution for the Euler equation. Firstly, we consider the generalization of the 2D Euler equation, i.e. the generalized surface quasi-geostrophic equation, we construct travelling and rotating solutions such that the active scalar has compact support. A key element in the construction is the non-degeneracy for the solutions of the fractional plasma equation. I will also talk about the 3D Euler equation, for which we construct travelling solutions of multiple vortex rings. This is based on joint work with Davila, Liu, Del Pino, Musso, Wei.