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arXiv · 2506.23868

A priori bounds and equicontinuity of orbits for the intermediate long wave equation

Benjamin Harrop-Griffiths·Rowan Killip·Monica Visan
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Abstract

We prove uniform-in-time a priori $H^s$ bounds for solutions to the intermediate long wave equation posed both on the line and on the circle, covering the range $-\frac12<s\leq0$. Additionally, we prove that the set of orbits emanating from a bounded and equicontinuous set in $H^s$ is also bounded and equicontinuous in $H^s$. Our proof is based on the identification of a suitable Lax pair formulation for the intermediate long wave equation.

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Benjamin Harrop-Griffiths, Rowan Killip, Monica Visan. 2025-06-30. A priori bounds and equicontinuity of orbits for the intermediate long wave equation. https://arxiv.org/abs/2506.23868

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