Classical Solutions of the Fornberg-Whitham Equation
Analysis of PDEs
2025-03-05 v3
Abstract
In this paper, we prove well-posedness in (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}
}