Abstract:This paper establishes a sharp, expanded wave-breaking criterion for a class of nonlinear nonlocal Whitham-type equations, significantly generalizing the classical threshold introduced by Seliger. While the system of inequalities governing the spatial extrema of the fluid deviation has been extensively studied, establishing a sharp condition has remained a challenge. This difficulty is primarily due to the non-cooperative nature of the system, which precludes the application of standard comparison principles. We rigorously overcome this analytical obstacle by identifying the exact nonlinear threshold that confines the solutions of the inequality system and analyzing its time evolution.
| Subjects: | Analysis of PDEs (math.AP) |
| MSC classes: | 35L05, 35B30 |
| Cite as: | arXiv:2605.24839 [math.AP] |
| (or arXiv:2605.24839v1 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24839 arXiv-issued DOI via DataCite (pending registration) |
From: Yongki Lee [view email]
[v1]
Sun, 24 May 2026 03:09:48 UTC (3,369 KB)
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