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arXiv · 1506.04075

Wave breaking in the Whitham equation

Vera Mikyoung Hur
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Abstract

We prove wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equation which combines the dispersion relation of water waves and a nonlinearity of the shallow water equations, provided that the slope of the initial datum is sufficiently negative, whereby we solve a Whitham's conjecture. We extend the result to equations of Korteweg-de Vries type for a range of fractional dispersion.

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Vera Mikyoung Hur. 2015-06-12. Wave breaking in the Whitham equation. https://arxiv.org/abs/1506.04075

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