DIVERGENCE-FREE VECTOR-FIELD AND REDUCTION

By the Lie symmetry group, the reduction for divergence-free vector-fi elds (DFVs) is studied, and the following results are found. A n-dimen sional DFV can be locally reduced to a (n - 1)-dimensional DFV if it a dmits a one-parameter symmetry group that is spatial and divergenceles s. More generally, a n-dimensional DFV admitting a r-parameter, spatia l, divergenceless Abelian (commutable) symmetry group can be locally r educed to a (n - r)-dimensional DFV. (C) 1998 Elsevier Science B.V.