TY - JOUR
T1 - A Note on “Small Amplitude Solutions of the Generalized  IMBq Equation”
AU - Youbin Zhu 
JO - Journal of Partial Differential Equations
VL - 4
SP - 377
EP - 383
PY - 2006
DA - 2006/11
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5340.html
KW - IMBq equation
KW - Duhamel's principle
KW - Hölder inequality
KW - Gronwall inequality
KW - Hausdorff-Young inequality
AB -  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 H^s 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.