Inserted: 4 feb 2007
Last Updated: 3 may 2011
Journal: Ann. of Math.
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 $R^n$ 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.
For the most updated version and eventual errata see the page
Keywords: differential inclusions, Euler equations, weak solutions