Global existence of small amplitude solution for the generalized IMBq equation |
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Authors: | Youbin Zhu |
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Institution: | Department of Mathematics, Xidian University, PO Box 245, Xi'an 710071, China |
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Abstract: | 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. |
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Keywords: | IMBq equation Duhamel's principle Hö lder inequality Gronwall inequality Hausdorff-Young inequality |
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