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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.
We prove dynamical dichotomy into scattering and blow-up (in a weak sense) for all radial solutions of the Zakharov system in the energy space of four spatial dimensions that have less energy than the ground state, which is written using the Aubin-Ta
We consider the global dynamics below the ground state energy for the Zakharov system in the 3D radial case. We obtain dichotomy between the scattering and the growup.
We prove scattering for the radial nonlinear Klein-Gordon equation $ partial_{tt} u - Delta u + u = -|u|^{p-1} u $ with $5 > p >3$ and data $ (u_{0}, u_{1}) in H^{s} times H^{s-1} $, $ 1 > s > 1- frac{(5-p)(p-3)}{2(p-1)(p-2)} $ if $ 4 geq p > 3 $ and
We prove small energy scattering for the 3D Zakharov system with radial symmetry. The main ingredients are normal form reduction and the radial-improved Strichartz estimates.
The two-dimensional Zakharov system is shown to have a unique global solution for data without finite energy if the L^2 - norm of the Schrodinger part is small enough. The proof uses a refined I-method originally initiated by Colliander, Keel, Staffi