Xia, Suxia; Yuan, Jia Existence and scattering of small solutions to a Boussinesq type equation of sixth order. (English) Zbl 1195.35229 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 4, 1015-1027 (2010). Summary: We consider the existence and uniqueness of the global small solution as well as the small data scattering result to the Cauchy problem for a Boussinesq type equation of sixth order with the nonlinear term \(f(u)\) behaving as \(u^p\) \((p>1)\) as \(u\to 0\) in \(\mathbb R^n\), \(n\geq 1\). The main method and techniques used in our paper are the Littlewood-Paley dyadic decomposition, the stationary phase estimate and some properties of Bessel functions. Cited in 9 Documents MSC: 35L76 Higher-order semilinear hyperbolic equations 35L30 Initial value problems for higher-order hyperbolic equations 35Q35 PDEs in connection with fluid mechanics Keywords:dispersive estimate; Littlewood-Paley dyadic decomposition PDFBibTeX XMLCite \textit{S. 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