Seminar Analysis and Mathematical Physics: Louise Gassot (IRMAR, Rennes)

Zero-dispersion limit for the Benjamin-Ono Equation

We focus on the Benjamin-Ono equation on the line with a small dispersion parameter. The goal of this talk is to precisely describe the solution at all times when the dispersion parameter is small enough. This solution may exhibit locally rapid oscillations, which are a manifestation of a dispersive shock. The description involves the multivalued solution of the underlying Burgers equation, obtained by using the method of characteristics. This work is in collaboration with Elliot Blackstone, Patrick Gérard, and Peter Miller.

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