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arXiv · 1805.06039

On sharp global well-posedness and Ill-posedness for a fifth-order KdV-BBM type equation

Mahendra Panthee·Xavier Carvajal
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Abstract

We consider the Cauchy problem associated to the recently derived higher order hamiltonian model for unidirectional water waves and prove global existence for given data in the Sobolev space $H^s$, $s\geq 1$. We also prove an ill-posedness result by showing that the flow-map is not continuous if the given data has Sobolev regularity $s< 1$. The results obtained in this work are sharp.

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Mahendra Panthee, Xavier Carvajal. 2019-06-26. On sharp global well-posedness and Ill-posedness for a fifth-order KdV-BBM type equation. https://arxiv.org/abs/1805.06039

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