Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in four and more spatial dimensions (Q334509)

This paper studies the Cauchy problem for the Klein-Gordon-Zakharov system in four and more spatial dimensions. As stated in the paper, such system provides the physical model for the interaction of the Langmuir wave and the ion acoustic wave in a plasma. The author considers both the radial case and the non-radial case. For the radial case, the author proves the small data global well-posedness and scattering at the critical space in dimension \(\geq 4\) by applying the radial Strichartz estimates and \(U^2\), \(V^2\) type spaces. For the non-radial case, the author obtains the local well-posedness result in dimension \(\geq 5\).NEWLINENEWLINEThe paper is divided into four sections. The first section provides introduction and statement of main results. The second section provides some preliminaries lemmas and propositions. The third section proves the bilinear estimates. The last section provides proofs of main results.