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arXiv · 1911.08440

$W^{1,\infty}$ instability of $H^1$-stable peakons in the Novikov equation

Robin Ming Chen·Dmitry E. Pelinovsky
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Abstract

It is known from the previous works that the peakon solutions of the Novikov equation are orbitally and asymptotically stable in $H^1$. We prove, via the method of characteristics, that these peakon solutions are unstable under $W^{1,\infty}$-perturbations. Moreover, we show that small initial $W^{1,\infty}$-perturbations of the Novikov peakons can lead to the finite time blow-up of the corresponding solutions.

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Robin Ming Chen, Dmitry E. Pelinovsky. 2019-11-19. $W^{1,\infty}$ instability of $H^1$-stable peakons in the Novikov equation. https://arxiv.org/abs/1911.08440

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