Date: Monday, January 10, 2022
Location: ZOOM ID: 926 6491 9790 Virtual (4:00 PM to 5:00 PM)
Title: Zero-dispersion limit for the Benjamin-Ono equation on the torus
Abstract: We discuss the zero-dispersion limit for the Benjamin-Ono equation on the torus given a single well initial data. We prove that there exist approximate initial data converging to the initial data, such that the corresponding solutions admit a weak limit as the dispersion parameter tends to zero. The weak limit is expressed in terms of the multivalued solution of the inviscid Burgers equation obtained by the method of characteristics. We construct our approximation by using the Birkhoff coordinates of the initial data, introduced by Gérard, Kappeler and Topalov. In the case of the cosine initial data, we completely justify this approximation by proving an asymptotic expansion of the Birkhoff coordinates.
A recording of the talk can be found here.
Files:
Speaker: Louise Gassot
Institution: ICERM
Event Organizer: Ahmad Barhoumi barhoumi@umich.edu
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