In this paper we focus on the Cauchy problem for a nonlinear wave equation of fourth-order in n-dimensional space (n ⩾ 1), the decay structure of which is of regularity-loss property. Based on the decay estimate of solutions to the linear problem, we introduce a set of time-weighted Sobolev spaces. By using the contraction mapping theorem, we obtain the global in-time existence and the optimal decay estimates of solutions to the Cauchy problem under smallness assumption on the initial data.
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