Well-posedness and wave breaking of the degenerate Novikov equation

In this paper, we investigate the degenerate Novikov equation, which is proposed as a scaling limit of the Novikov equation, and is integrable since it admits bi-Hamiltonian structure and Lax-pair. Geometrically, it arises from an intrinsic space curve flow in the centro-equiaffine geometry. In the periodic setting, local well-posedness of the initial value problem to the equation in the Sobolev space is established via Kato's theory. It turns out that singularities of the solutions occur only in the form of wave-breaking. A sufficient condition on initial data is obtained to guarantee the formation of singularities. Finally, a kind of singular solutions are also presented.