Global existence of small amplitude solution for the generalized IMBq equation

In this paper, we reconsider the problem discussed in [G.W. Chen, S.B. Wang, Small amplitude solutions of the generalized IMBq equation, J. Math. Anal. Appl. 274 (2002) 846–866]. The proof of global existence presented in [G.W. Chen, S.B. Wang, Small amplitude solutions of the generalized IMBq equation, J. Math. Anal. Appl. 274 (2002) 846–866] is very simple in form, but it is a pity that the authors overlooked the bad behavior of low frequency part of B(t)ψ which causes trouble in L∞ and Hs estimates. In this paper, we will give out a new proof of the global existence under an additional condition on the initial data.