Well-posedness and scattering for the Zakharov system in four dimensions

TL;DR

This paper establishes well-posedness and scattering results for the four-dimensional Zakharov system, including for small initial data in energy space, without symmetry restrictions.

Contribution

It provides new global well-posedness and scattering results for the 4D Zakharov system, extending previous work to non-radial data and energy space initial conditions.

Findings

Global well-posedness for small initial data

Scattering results in energy space

No symmetry restrictions required

Abstract

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 is restricted to radially symmetric data.