Well-posedness of a highly nonlinear shallow water equation on the circle

Official URL: http://dx.doi.org/10.1016/j.na.2020.111849

We present a comprehensive introduction and overview of a recently derived model equation for waves of large amplitude in the context of shallow water waves and provide a literature review of all the available studies on this equation. Furthermore, we establish a novel result concerning the local well-posedness of the corresponding Cauchy problem for space-periodic solutions with initial data from the Sobolev space H-s on the circle for s > 3/2.