THE EULER EQUATIONS AS A DIFFERENTIAL INCLUSION

Abstract. In this paper we propose a new point of view on weak so-lutions of the Euler equations, describing the motion of an ideal incom-pressible fluid in Rn with n ≥ 2. We give a reformulation of the Euler equations as a differential inclusion, and in this way we obtain transpar-ent 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. 1