  We consider here the local existence of strong solutions for the
Zakharov-Kuznestov (ZK) equation posed in a limited domain (0,1)_{x}\times(-pi
/2, pi /2)^d, d=1,2. We prove that in space dimensions 2 and 3, there exists a
strong solution on a short time interval, whose length only depends on the
given data. We use the parabolic regularization of the ZK equation to derive
the global and local bounds independent of epsilon for various norms of the
solution. In particular, we derive the local bound of the nonlinear term by a
singular perturbation argument. Then we can pass to the limit and hence deduce
the local existence of strong solutions.
