%0 Journal Article
%T Inviscid symmetry breaking with non-increasing energy
%A Emil Wiedemann
%J Mathematics
%D 2013
%I arXiv
%X In a recent article, C. Bardos et. al. constructed weak solutions of the three-dimensional incompressible Euler equations which emerge from two-dimensional initial data yet become fully three-dimensional at positive times. They asked whether such symmetry-breaking solutions could also be constructed under the additional condition that they should have non-increasing energy. In this note, we give a positive answer to this question and show that such a construction is possible for a large class of initial data. We use convex integration techniques as developed by De Lellis-Sz\'ekelyhidi.
%U http://arxiv.org/abs/1310.5925v1