Scattering and well-posedness for the Zakharov system at a critical space in four and more spatial dimensions

Isao Kato, Kotaro Tsugawa

We study the Cauchy problem for the Zakharov system in spatial dimension $d\ge 4$ with initial datum $(u(0), n(0), \partial_t n(0)) \in H^k(\mathbb{R}^d) \times \dot{H}^l(\mathbb{R…