TITLE: Compressible Ebin-Marsden?
QUESTION [8 upvotes]: In Ebin and Marsden's paper Groups of Diffeomorphisms and the Motion of an Incompressible Fluid, there is a footnote on the first page indicating that non-homogeneous cases and the case of compressible fluid mechanics will be treated in a forthcoming paper.
Having taken a search through MathSciNet I did not see anything obvious as the mentioned followup. Does anyone have a reference as to which paper that is referring to?

REPLY [6 votes]: The compressible case uses semidirect products of groups (group of diffeomorphisms times functions).
To my knowledge, the first paper that discusses this in detail is
Marsden, Ratiu, Weinstein: Semidirect Products and Reduction in Mechanics (PDF).
There the authors state

By 1980 it was known that the equations for compressible flow on R3 were
formally Lie-Poisson equations for the semidirect product...

So even back then it was already folklore.