A NOTE ON "SMALL AMPLITUDE SOLUTIONS OF THE GENERALIZED IMBQ EQUATION"

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: IMBq equation Duhamel's principle H(o)lder inequality Gronwall inequality Hausdorff-Young inequality.
• 年，卷（期）: 2006,（4）
• 页码范围: 377-383
• 页数: 7页
• 分类号: O175.24
• 语种: 英文

摘要

Global existence of small amplitude solution and nonlinear scattering result for the Cauchy problem of the generalized IMBq equation were considered in the paper titled "Small amplitude solutions of the generalized IMBq equation" [1]. It is a pity that the authors overlooked the bad behavior of low frequency part of S(t)ψ which causes troubles in L∞ and Hs estimates. In this note, we will present a new proof of global existence under same conditions as in [1] but for space dimension n ≥ 3.