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We demonstrate norm inflation for nonlinear nonlocal equations, which extendthe Korteweg-de Vries equation to permit fractional dispersion, in the periodicand non-periodic settings. That is, an initial datum is smooth and arbitrarilysmall in a Sobolev space, but the solution becomes arbitrarily large in theSobolev space after an arbitrarily short time.

Norm inflation for equations of KdV type with fractional dispersion