Lower bounds for the blowup rate of solutions of the Zakharov equation in dimension two

We consider the blowup solution (u,n,v)(t) of the Zakharov equations where u: R2 → C, n: R2 → R, v: R2 → R2 in the energy space H1 = {(u,n,v) η H1 × L2 × L2}. We show that there is a constant c depending on the L2-norm of u0 such that where T is the blowup time. We check that this estimate is optimal and give further applications.