Asymptotic behavior of solution of Whitham–Broer–Kaup type equations with negative dispersion

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+β2<0 as well as the convergence to 0 of small solutions at rate O(t−1/2) .