In this paper, well prove a L^2-concentration result of Zakharov system in space dimension two, with radial initial data (u_0,n_0,n_1)in H^stimes L^2times H^{-1} ({16/17}<s<1), when blow up of the solution happens by I-method. In additional to that we find a blow up character of this system. Furthermore, we improve the global existence result of Bourgains to above spaces.
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