Rigorous estimates on mechanical balance laws in the Boussinesq–Peregrine equations

Abstract

It is shown that the Boussinesq–Peregrine system, which describes long waves of small amplitude at the surface of an inviscid fluid with variable depth, admits a number of approximate conservation equations. Notably, this paper provides accurate estimations for the approximate conservation of the mechanical balance laws associated with mass, momentum, and energy. These precise estimates offer valuable insights into the behavior and dynamics of the system, shedding light on the conservation principles governing the wave motion.

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

“…The second and third integral are sometimes called momentum and energy, but this terminology may be misleading since these integrals are not readily interpreted as approximations of the physical momentum and energy appearing in the context of the Euler equations. Indeed, the authors of [1] already state clearly that they do not believe these integrals to be approximations of the physical momentum and density, and further doubt was cast on this interpretation in more recent work [2,19,20,23].…”