Fuzzy Fluid Mechanics in Three Dimensions

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Rajeev, S. G.
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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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Mathematical Physics, Condensed Matter - Statistical Mechanics, General Relativity and Quantum Cosmology, High Energy Physics - Theory, Mathematics - Analysis of PDEs, Mathematics - Quantum Algebra, Nonlinear Sciences - Chaotic Dynamics, Physics - Fluid Dynamics
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