Résumé
We update here the results on the decay of solutions to a nonlocal water wave equation that reads $$u_t+u_x+\frac{1}{\sqrt{\pi}}\frac{\partial}{\partial t}\int_0^t\frac{u(s)}{\sqrt{t−s}}ds+uu_x=u_{xx}$$ where $$\frac{1}{\sqrt{\pi}}\frac{\partial}{\partial t}\int_0^t\frac{u(s)}{\sqrt{t−s}}ds$$ is the Riemann–Liouville half-order derivative.