Complete integrability of a hydrodynamic Navier-Stokes model of the flow in a two-dimensional incompressible ideal liquid with a free surface

Abstract

We establish the complete integrability of a nonlinear dynamical system associated with the hydrodynamic Navier-Stokes equations for the flow of an ideal two-dimensional liquid with a free surface over the horizontal bottom. We show that this dynamical system is naturally connected with the nonlinear kinetic Boltzmann-Vlasov equation for a one-dimensional flow of particles with a point potential of interaction between particles.