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We introduce many families of explicit solutions to the three dimensionalincompressible Euler equations for nonviscous fluid flows using the Lagrangianframework. Almost no exact Lagrangian solutions exist in the literature priorto this study. We search for solutions where the time component and the spatialcomponent are separated, applying the same ideas we used previously in the twodimensional case. We show a general method to derive separate constraintequations for the spatial component and the time component. Using this providesus with a plenty of solution sets exhibiting several different types of fluidbehaviour, but since they are computationally heavy to analyze, we have torestrict deeper analysis to the most interesting cases only. It is alsopossible and perhaps even probable that there exist more solutions of theseparation of variables type beyond what we have found.

Explicit solutions to the 3D incompressible Euler equations in Lagrangian formulation