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On the well-posedness of the hyperelastic rod equation
Published 3 Nov 2016 in math.AP | (1611.01188v1)
Abstract: In this paper we consider the hyperelastic rod equation on the Sobolev spaces $Hs(\R)$, $s > 3/2$. 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 $Hs(\mathbb T)$, $s > 3/2$.
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