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arXiv · 2604.12423

Norm inflation and low-regularity ill-posedness for the rod equation

Jinlu Li·Yanghai Yu
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Abstract

In this paper, we consider the Cauchy problem for the rod equation in the line. By constructing an explicit smooth initial data, we present a new method to prove that this problem is ill-posed in $H^s(\R)$ with $1< s<3/2$ in the sense of {\it norm inflation}, i.e., an initial data is smooth and arbitrarily small in $H^s(\R)$ with $1< s<3/2$, but the solution becomes arbitrarily large in the Sobolev space after an arbitrarily short time.

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Jinlu Li, Yanghai Yu. 2026-04-14. Norm inflation and low-regularity ill-posedness for the rod equation. https://arxiv.org/abs/2604.12423

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