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arXiv · 1810.10434

On the ill-posedness of the 5th-order Gardner equation

Miguel A. Alejo·Eleomar Cardoso Jr
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Abstract

We present ill-posedness results for the initial value problem (IVP) of the 5th-order Gardner equation. We use new breather solutions discovered for this higher order Gardner equation to measure the regularity of the Cauchy problem in Sobolev spaces $H^s$. We find the sharp Sobolev index under which the local well-posedness of the problem is lost, meaning that the dependence of 5th order Gardner solutions upon initial data fails to be continuous.

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Miguel A. Alejo, Eleomar Cardoso Jr. 2018-10-24. On the ill-posedness of the 5th-order Gardner equation. https://arxiv.org/abs/1810.10434

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