Speaker: Henrik Kalisch, University of Bergen
Date: November 12, 2015
Title: Balance Laws for Dispersive Long Wave Equations
Abstract: Dispersive long wave models, such as the KdV equation and a variety of Boussinesq and Green-Naghdi systems can be shown to accurately describe wave motion at the surface of a homogeneous fluid if the waves have small amplitude and are sufficiently long. All these model equations feature constants of motion in the form of time-invariant integrals. Some approximate models, such as the KdV equation admit an infinite number of conserved integrals. However, the physical meaning of these integrals is relatively poorly understood.
In this lecture, we look at how energy conservation and other balance laws of the Euler equations may be represented in the context of these approximate models, and how they are connected to the invariant integrals of the model equations.