Priscila Da Silva - Existence and uniqueness of solutions for the rotation-Camassa-Holm equation

Since the discovery of the Camassa-Holm equation as an integrable peakon-equation, intense research has been dedicated to its generalisations and to the study of the corresponding solutions. Of particular interest in this talk is the rotation-Camassa-Holm equation (rCH), a nonlocal evolutionary equation that takes into consideration the Coriolis force, which is typically a manifestation of rotation when Newton's laws are applied to model physical phenomena on Earth's surface. In this talk we present conditions for the existence of traveling wave solutions and show that, given an initial data in Sobolev spaces, uniqueness of local solutions is achieved. Moreover, assuming a strong condition on the McKean quantity, the solutions can be extended globally. Extensions of these results are presented, as well as further conjectures.