Katie Massey
The Ohio State University
Title
Hölder Continuity of the RZQ Equation.
Abstract
In 1993, Camassa and Holm introduced an integrable PDE to model nonlinear shallow water waves. In contrast to the classical Korteweg–de Vries equation, whose solutions are smooth solitons, solutions to CH-type equations are peaked solitons, appropriately dubbed “peakons”. In this talk, we will study a new integrable fifth-order CH–type equation, which we call the RZQ equation after its developers Reyes, Zhu, and Qiao. The initial value problem corresponding to this equation is well-posed in Sobolev spaces $H^s$ for s > 7/2, and solutions take the form of “pseudo-peakons”, which are structurally similar to peakon solutions but analytically forgiving. Though the data-to-solution map is not uniformly continuous in the $H^s$ topology, it is Hölder continuous in weaker $H^r$ norms. My focus will be to establish such continuity and highlight where it contrasts continuity results of similar equations.