Abstract
Abstract In this work, we discuss the long time behavior of solutions of the Whitham–Broer–Kaup system with Lipschitz nonlinearity and negative dispersion term. We prove the global well-posedness when α + β 2 < 0 {\alpha+\beta^{2}<0} as well as the convergence to 0 of small solutions at rate 𝒪 ( t - 1 / 2 ) {\mathcal{O}(t^{-1/2})} .
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