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

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 $s>3/2$.

References in corpus (2)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Inverse Scattering Transform for the Degasperis-Procesi Equation

Cited by in corpus (1)

• Shallow-water equations with complete Coriolis force: Group Properties and Similarity Solutions