# Convexity of Whitham's highest cusped wave

@article{Enciso2018ConvexityOW, title={Convexity of Whitham's highest cusped wave}, author={A. Enciso and Javier G'omez-Serrano and B. Vergara}, journal={arXiv: Analysis of PDEs}, year={2018} }

We prove the existence of a periodic traveling wave of extreme form of the Whitham equation that has a convex profile between consecutive stagnation points, at which it is known to feature a cusp of exactly $C^{1/2}$ regularity. The convexity of Whitham's highest cusped wave had been conjectured by Ehrnstr\"om and Wahl\'en.

#### 3 Citations

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