Global well-posedness and scattering for the Zakharov system at the critical space in three spatial dimensions with small and radial initial data (Q2084861)

The authors study small, radial solutions of the Zakharov system modeling the Langmuir turbulence in plasmas in the three-dimensional case. The main result is the global well-posedness of the Cauchy problem obtained for small and radial initial data in the critical Sobolev spaces. Moreover, scattering is shown for such solutions. The use of radial Strichartz estimates is an essential ingredient of the proofs.