Classical existence and regularity results can be found in the survey http://arxiv.org/abs/math/0703406 (Euler Equations of Incompressible Ideal Fluids, by C. Bardos and E. S. Titi -- http://www.mccme.ru/~ansobol/otarie/slides/Russ-Math-Surveys-Euler-Bardos.pdf is the published version).
P.S. This paper http://arxiv.org/abs/1402.4957 (Cauchy's almost forgotten Lagrangian formulation of the Euler equation for 3D incompressible flow, by Uriel Frisch and Barbara Villone) gives some very interesting historical background about 3D Euler equation.