Existence and uniqueness of solutions with low regularity for a class of nonlinear dispersive equations

Abstract

Working in Lagrangian coordinates, we prove the existence and uniqueness of solutions for a class of periodic nonlinear dispersive equations with continuously differentiable initial data. This lowers the regularity requirements available for the Cauchy problem by means of the semigroup approach for quasi-linear hyperbolic equations of evolution or by the viscosity method.