Convergence of mechanical balance laws for water waves: from KdV to Euler

Abstract

This article takes into account the Korteweg–de Vries (KdV) equation as an approximate model of long waves of small amplitude at the free surface with inviscid fluid. It is demonstrated that the mechanical balance quantities, as defined by the solution of the KdV equation, rigorously approximate those in the Euler system within the L ∞ space. Furthermore, these approximations are estimated in relation to the parameter ε characterizing the long-wave behavior.