  The study of the 2D Euler equation with non Lipschitzian velocity was
initiated by Yudovich in [19] where a result of global well-posedness for
essentially bounded vorticity is proved. A lot of works have been since
dedicated to the extension of this result to more general spaces. To the best
of our knowledge all these contributions lack the proof of at least one of the
following three fundamental properties: global existence, uniqueness and
regularity persistence. In this paper we introduce a Banach space containing
unbounded functions for which all these properties are shown to be satisfied.
