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Integrable Systems and Random Matrix Theory Seminar

Zero-dispersion limit for the Benjamin-Ono equation on the torus
Monday, January 10, 2022
4:00-5:00 PM
ZOOM ID: 926 6491 9790 Off Campus Location
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. Speaker(s): Louise Gassot (ICERM)
Building: Off Campus Location
Location: Virtual
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics