2007/02/28 by Camillo De Lellis, László Székelyhidi Jr · 1 citation
Mathematics · #math.AP #msc:76B03 #msc:35D05 #msc:76F99
published as Ann. of Math. (2) 170 (2009), no. 3, 1417-1436 · 16 pages; v2: corrected typos, simplified some proofs; v3: 20 pages, added a second (more direct) proof
arxiv created 2007/11/27 · arxiv updated 2011/05/06
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 ℝn with n≥ 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.