On admissibility criteria for weak solutions of the Euler equations

2007/12/31 by Camillo De Lellis, László Székelyhidi Jr · 2 citations
Mathematics · #math.AP #msc:76B03 #msc:35D05 #msc:76F99

paper · pdf · doi:10.1007/s00205-008-0201-x

published as Arch. Ration. Mech. Anal. 195 (2010), no. 1, 225-260 · 33 pages, 1 figure; v2: 35 pages, corrected typos, clarified proofs

arxiv created 2008/09/26 · arxiv updated 2015/05/12

Abstract

We consider solutions to the Cauchy problem for the incompressible Euler equations satisfying several additional requirements, like the global and local energy inequalities. Using some techniques introduced in an earlier paper we show that, for some bounded compactly supported initial data, none of these admissibility criteria singles out a unique weak solution. As a byproduct we show bounded initial data for which admissible solutions to the p-system of isentropic gas dynamics in Eulerian coordinates are not unique in more than one space dimension.

Cited by

• Global regularity for the Navier-Stokes equations with application to global solvability for the Euler equations
• Path-connectedness of incompressible Euler solutions