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arXiv · 2212.08159

Classical Solutions of the Fornberg-Whitham Equation

Georgia Burkhalter·Ryan C. Thompson·Madison Waldrep
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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.

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Georgia Burkhalter, Ryan C. Thompson, Madison Waldrep. 2022-12-15. Classical Solutions of the Fornberg-Whitham Equation. https://doi.org/10.2140/involve.2025.18.239

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