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arXiv · 2607.13259

Ill-posedness in the critical Sobolev space for the Fokas-Olver-Rosenau-Qiao equation

Dan-Andrei Geba
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Abstract

This article proves norm inflation in the critical Sobolev space $H^{5/2}(\mathbb{R})$ for the Fokas-Olver-Rosenau-Qiao equation, which is a modified Camassa-Holm-type equation with cubic nonlinearity. This result complements the well-posedness theory for this equation, which was previously known to be locally well-posed in $H^{s}(\mathbb{R})$ for $s>5/2$. The proof relies on the construction of explicit initial data satisfying the previously known blow-up criteria for the Fokas-Olver-Rosenau-Qiao equation, a step that appears to be of independent interest.

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Dan-Andrei Geba. 2026-07-14. Ill-posedness in the critical Sobolev space for the Fokas-Olver-Rosenau-Qiao equation. https://arxiv.org/abs/2607.13259

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