Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in five and more dimensions

Abstract

We study the Cauchy problem of the Klein-Gordon-Zakharov system in spatial dimension $d\ge 5$ with initial datum $(u,{\partial }_{t}u,n,{\partial }_{t}n){|}_{t=0}\in H^{s+1}({\mathbb{R}}^d)\times H^s({\mathbb{R}}^d)\times {\dot{H}}^s({\mathbb{R}}^d)\times {\dot{H}}^{s-1}({\mathbb{R}}^d)$. The critical value of $s$ is $s_c=d/2-2$. By $U^2,V^2$ type spaces, we prove that the small data global well-posedness and scattering hold at $s=s_c$ in $d\ge 5$.

arXiv admin note: substantial text overlap with arXiv:1512.01510

References in corpus (2)

• Convolutions of singular measures and applications to the Zakharov system
• Global existence without decay for quadratic Klein-Gordon equations