  We consider a state-of-the-art ferroelectric phase-field model arising from
the engineering area in recent years, which is mathematically formulated as a
coupled elliptic-parabolic differential system. We utilize a fixed point
theorem based on the maximal parabolic regularity theory to show the local in
time well-posedness of the ferroelectric problem. The well-posedness result
will firstly be proved under certain general assumptions. We then give precise
geometric and regularity conditions which will guarantee the fulfillment of the
assumptions.
