On Well-Posedness of Nonlocal Evolution Equations

This work studies questions of existence, uniqueness, dependence on initial data, and regularity of solutions to the Cauchy problem for nonlocal evolution equations with data in Sobolev spaces. The focus is on integrable Camassa–Holm type equations and in particular the Novikov equation and its dispersive modification. These equations apart from being interesting on their own right, also they can serve as “toy” models for the Euler equations.