Published Paper
Inserted: 27 dec 2007
Last Updated: 3 may 2011
Journal: Arch. Ration. Mech. Anal.
Volume: 195
Pages: 225-260
Year: 2010
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.
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Keywords: conservation laws, differential inclusions, Euler equations, energy inequality