  In this paper we study the Novikov-Veselov equation and the related modified
Novikov-Veselov equation in certain Sobolev spaces. We prove local
well-posedness in H^s (R2) for s > 1/2 for the Novikov-Veselov equation, and
local well-posedness in H^s (R2) for s > 1 for the modified Novikov-Veselov
equation. Finally we point out some ill-posedness issues for the Novikov-
Veselov equation in the supercritical regime.
