English

Classical Solutions of the Fornberg-Whitham Equation

Analysis of PDEs 2025-03-05 v3

Abstract

In this paper, we prove well-posedness in C1(R)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.

Keywords

Cite

@article{arxiv.2212.08159,
  title  = {Classical Solutions of the Fornberg-Whitham Equation},
  author = {Georgia Burkhalter and Ryan C. Thompson and Madison Waldrep},
  journal= {arXiv preprint arXiv:2212.08159},
  year   = {2025}
}