Fuzzy Fluid Mechanics in Three Dimensions
Mathematical Physics
2016-09-08 v2 Statistical Mechanics
General Relativity and Quantum Cosmology
High Energy Physics - Theory
Analysis of PDEs
math.MP
Quantum Algebra
Chaotic Dynamics
Fluid Dynamics
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.
Cite
@article{arxiv.0705.2139,
title = {Fuzzy Fluid Mechanics in Three Dimensions},
author = {S. G. Rajeev},
journal= {arXiv preprint arXiv:0705.2139},
year = {2016}
}