  We introduce many families of explicit solutions to the three dimensional
incompressible Euler equations for nonviscous fluid flows using the Lagrangian
framework. Almost no exact Lagrangian solutions exist in the literature prior
to this study. We search for solutions where the time component and the spatial
component are separated, applying the same ideas we used previously in the two
dimensional case. We show a general method to derive separate constraint
equations for the spatial component and the time component. Using this provides
us with a plenty of solution sets exhibiting several different types of fluid
behaviour, but since they are computationally heavy to analyze, we have to
restrict deeper analysis to the most interesting cases only. It is also
possible and perhaps even probable that there exist more solutions of the
separation of variables type beyond what we have found.
