Abstract
For \(s 1\). The proof of ill-posedness depends on the value of b, where the most interesting case arises for \(b=3\), the Degasperis–Procesi equation. Considering that the b-family of equations is locally well-posed in \(H^s\) for \(s>3/2\), this work establishes 3 / 2 as the critical index of well-posedness in Sobolev spaces for \(b>1\).
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