  We introduce a rotation invariant short distance cut-off in the theory of an
ideal fluid in three space dimensions, by requiring momenta to take values in a
sphere. This leads to an algebra of functions in position space is
non-commutative. Nevertheless it is possible to find appropriate analogues of
the Euler equations of an ideal fluid. The system still has a hamiltonian
structure. It is hoped that this will be useful in the study of possible
singularities in the evolution of Euler (or Navier-Stokes) equations in three
dimensions.
