On the well-posedness of the hyperelastic rod equation

In this paper we consider the hyperelastic rod equation on the Sobolev spaces $H^s(\R)$, $s > 3/2$. Using a geometric approach we show that for any $T > 0$ the corresponding solution map, $u(0) \mapsto u(T)$, is nowhere locally uniformly continuous. The method applies also to the periodic case $H^s(\mathbb T)$, $s > 3/2$.

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