  Whereas Holm proved that the ring of differential operators on a generic
hyperplane arrangement is finitely generated as an algebra, the problem of its
Noetherian properties is still open. In this article, after proving that the
ring of differential operators on a central arrangement is right Noetherian if
and only if it is left Noetherian, we prove that the ring of differential
operators on a central 2-arrangement is Noetherian. In addition, we prove that
its graded ring associated to the order filtration is not Noetherian when the
number of the consistuent hyperplanes is greater than 1.
