The Cauchy problem for the Zakharov system in four dimensions is considered. Some new well-posedness results are obtained. For small initial data, global well-posedness and scattering results are proved, including the case of initial data in the energy space. None of these results are restricted to radially symmetric data.
"Well-posedness and scattering for the Zakharov system in four dimensions." Anal. PDE 8 (8) 2029 - 2055, 2015. https://doi.org/10.2140/apde.2015.8.2029