Classical Solutions of the Fornberg-Whitham Equation

Abstract

In this paper, we prove well-posedness in $C^1(\mathbb{R})$ (a.k.a. classical solutions) of the Fornberg-Whitham equation. To achieve this objective, we study its weak formulation under a Lagrangian framework. Applying the fundamental theorem of ordinary differential equations to the generated semi-linear system, we then construct a unique solution to the equation that is continuously dependent on the initial data. These results improve upon others in Sobolev and Besov spaces.

References in corpus (1)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations