Well-posedness of a highly nonlinear shallow water equation on the circle. (August 2020) - Duruk Mutlubas, Nilay; Geyer, Anna; Quirchmayr, Ronald
Abstract: 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 .