We study the global existence and decay rates of the Cauchy problem for the generalized Benjamin–Bona–Mahony equations in multi-dimensional spaces. By using Fourier
analysis, frequency decomposition, pseudo-differential operators and the energy method, we
obtain global existence and optimal L2 convergence rates of the solution.

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• GLOBAL EXISTENCE AND DECAY RATES OF SOLUTIONS OF GENERALIZED BENJAMIN–BONA–MAHONY EQUATIONS IN MULTIPLE DIMENSIONS