DOI: http://dx.doi.org/10.18273/revint.v34n1-2016004

Well-posedness and computation of solutions
of a regularized Benjamin-Ono system

FELIPE ALEXANDER PIPICANO, JUAN CARLOS MUÑOZ GRAJALES^*

Universidad del Valle, Departamento de Matemáticas, Cali, Colombia.

Abstract. This article is concerned with the existence and uniqueness of solutions of the Cauchy problem in the periodic setting for a regularized Benjamin-Ono type system (rBO) by using semigroup theory, Fourier analysis and Banach's fixed point theorem. This system was recently derived by Muñoz [12] as a weakly dispersive model for the propagation of small amplitude internal waves at the interface of two immiscible fluids with constant densities. We also conduct some numerical experiments to analyze the error and convergence in time and space of a fully discrete Fourier spectral scheme, for approximating the solutions of the initial value problem associated to the rBO system.

Keywords: Regularized BO system, internal waves, periodic travelling wave solutions, spectral methods.
MSC2010: 42A45, 47A75, 35Q51, 76M45.

El buen planteamiento y el cálculo de soluciones
de un sistema regularizado de Benjamin-Ono

Resumen. En este artículo se estudia la existencia y la unicidad de soluciones del problema de Cauchy, en el caso periódico, para un sistema de tipo Benjamin-Ono regularizado (rBO), usando teoría de semigrupos, análisis de Fourier y el Teorema del punto fijo de Banach. Este sistema fue deducido recientemente por Muñoz [12] como un modelo débilmente dispersivo para la propagación de ondas internas con pequeña amplitud en la interface de dos fluidos inmiscibles con densidades constantes. Además se realizan algunos experimentos numéricos para analizar el error y la convergencia en tiempo y espacio de un esquema espectral de Fourier completamente discreto, a fin de aproximar las soluciones del problema de valor inicial asociado con el sistema rBO.

Palabras clave: Sistema BO regularizado, ondas internas, soluciones de onda viajera periódicas, métodos espectrales.

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^*E-mail: juan.munoz@correounivalle.edu.co.
Received: 15 October 2015, Accepted: 05 February 2016.
To cite this article: F.A. Pipicano, J.C. Muñoz Grajales, Well-posedness and computation of solutions of a regularized Benjamin-Ono system, Rev. Integr. Temas Mat. 34 (2016), No. 1, 59-80.