On the zero-dispersion limit of the Benjamin-Ono Cauchy problem for positive initial data

Abstract

We study the Cauchy initial-value problem for the Benjamin-Ono equation in the zero-disperion limit, and we establish the existence of this limit in a certain weak sense by developing an appropriate analogue of the method invented by Lax and Levermore to analyze the corresponding limit for the Korteweg-de Vries equation.

54 pages, 11 figures

References in corpus (1)

• Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach