In this talk, we will study unbounded solutions of the incompressible Euler equations in two dimensions of space. The main interest of these solutions is that the usual function spaces in which solutions are defined (for example based on finite energy conditions like $L^2$ or $H^s$) are not compatible with the symmetries of the problem, namely Galileo invariance and scaling transformation. In addition, many real world problems naturally involve infinite energy solutions, typically in geophysics. After presenting the problem and giving an overview of previous results, we will state our result: existence and uniqueness of global Yudovich solutions under a certain sublinear growth assumption of the initial data. The proof is based on an integral decomposition of the pressure and local energy balance, leading to global estimates in local Morrey spaces. This work was done in collaboration with Herbert Koch (Universität Bonn).