The Zakharov system in 4D radial energy space below the ground state

We prove dynamical dichotomy into scattering and blow-up (in a weak sense) for all radial solutions of the Zakharov system in energy space four spatial dimensions that have less than ground state, which is written using Aubin-Talenti function. The characterized by critical mass wave component state. result similar to Kenig Merle energy-critical nonlinear Schr\"odinger equation (NLS). Unlike NLS, however, most difficult interaction proof stems from free component. In order control it, main novel ingredient we develop this paper uniform global Strichartz estimate linear with potential subcritical solving equation. This estimate, as well proof, may be independent interest. For follow idea Dodson Murphy.