Existence and Numerical Approximation of Solutions of an Improved Internal Wave Model

Abstract

In this paper we establish local existence of solutions for a new model to describe the propagation of an internal wave propagating at the interface of two immiscible fluids with constant densities, contained at rest in a long channel with a horizontal rigid top and bottom. We also introduce a spectral-type numerical scheme to approximate the solutions of the corresponding Cauchy problem and perform a complete error analysis of the semidiscrete scheme.

Keywords:

• internal waves
• Cauchy problem
• numerical solution
• error estimates

AMS Subject Classification:

• 65M70
• 65M70
• 35Q35
• 76B55