PDE och tillämpningar: Convexity of Whitam's wave of extreme form

  • Datum:
  • Plats: Ångströmlaboratoriet 64119
  • Föreläsare: Bruno Vergara, ICMAT
  • Kontaktperson: Kaj Nyström
  • Seminarium

Abstract: Whitham's model of shallow water waves is a non-local dispersive equation featuring travelling wave solutions as well as singularities. In this talk we will be interested in a conjecture of Ehrnström and Wahlen on the profile of solutions of extreme form to this equation. We will see that there exists a highest, cusped and periodic solution that is convex between consecutive peaks, where $C^{1/2}$-regularity has been shown to be optimal. The talk is based on joint work with A. Enciso and J. Gomez-Serrano.