Fuzzy Fluid Mechanics in Three Dimensions
arXiv:0705.2139 · doi:10.1142/S0217751X08038615
Abstract
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.
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