  This paper investigates the well posedness of ordinary differential equations
and more precisely the existence (or uniqueness) of a flow through explicit
compactness estimates. Instead of assuming a bounded divergence condition on
the vector field, a compressibility condition on the flow (bounded jacobian) is
considered. The main result provides existence under the condition that the
vector field belongs to $BV$ in dimension 2 and $SBV$ in higher dimensions.
