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.