  In this paper we propose a new point of view on weak solutions of the Euler
equations, describing the motion of an ideal incompressible fluid in
$\mathbb{R}^n$ with $n\geq 2$. We give a reformulation of the Euler equations
as a differential inclusion, and in this way we obtain transparent proofs of
several celebrated results of V. Scheffer and A. Shnirelman concerning the
non-uniqueness of weak solutions and the existence of energy--decreasing
solutions. Our results are stronger because they work in any dimension and
yield bounded velocity and pressure.
