Abstract
We introduce a rotation invariant short distance cutoff 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 that is noncommutative. 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.
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