  We consider the incompressible Euler and Navier-Stokes equations in a
three-dimensional moving thin domain. Under the assumption that the moving thin
domain degenerates into a two-dimensional moving closed surface as the width of
the thin domain goes to zero, we give a heuristic derivation of singular limit
equations on the degenerate moving surface of the Euler and Navier-Stokes
equations in the moving thin domain and investigate relations between their
energy structures. We also compare the limit equations with the Euler and
Navier-Stokes equations on a stationary manifold, which are described in terms
of the Levi-Civita connection.
