  The present paper is devoted to the study of the well-posedness and the lower
bound of blow-up rate to the Cauchy problem of the generalized Zakharov(GZ)
equations with magnetic field in R^d. The work of well-posedness of the GZ
system bases on the local well-posedness theory in [9]. At first, the
existence, uniqueness and continuity of solution to the GZ system with magnetic
field in Rd is proved. Next, we establish the lower bound of blow-up rate of
blow-up solution in sobolev spaces to the GZ system, which is almost a critical
index. Finally, we obtain the long time behavior of global solution,whose
H^k-norm grows at k-exponentially in time.
