Bruno Vergara: Convexity of Whitham's highest cusped wave

Abstract: In this talk I will discuss a conjecture of Ehrnstr\"om and Wahl\'en on the profile of travelling wave solutions of extreme form to Whitham's non-local dispersive equation. We will see that there exists a highest, cusped and periodic solution that is convex between consecutive crests, at which \(C^{1/2}\)-regularity has been shown to be optimal. The talk is based on joint work with A. Enciso and J. G\'omez-Serrano.