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

2016/12/09 by Isao Kato, Kato, Isao, Shinya Kinoshita +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1612.04240

Abstract

We study the Cauchy problem of the Klein-Gordon-Zakharov system in spatial dimension d ≥ 5 with initial datum (u, ∂_t u, n, ∂_t n)|_t=0 ∈ H^s+1(ℝ^d) × H^s(ℝ^d) × H^s(ℝ^d) × H^s-1(ℝ^d). The critical value of s is s_c=d/2-2. By U², V² type spaces, we prove that the small data global well-posedness and scattering hold at s=s_c in d ≥ 5.

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