  We study explicit solutions to the 2 dimensional Euler equations in the
Lagrangian framework. All known solutions have been of the separation of
variables type, where time and space dependence are treated separately. The
first such solutions were known already in the 19th century. We show that all
the solutions known previously belong to two families of solutions and
introduce three new families of solutions. It seems likely that these are all
the solutions that are of the separation of variables type.
