We demonstrate norm inflation for nonlinear nonlocal equations, which extend the Korteweg-de Vries equation to permit fractional dispersion, in the periodic and non-periodic settings. That is, an initial datum is smooth and arbitrarily small in a Sobolev space but the solution becomes arbitrarily large in the Sobolev space after an arbitrarily short time.
Vera Mikyoung Hur. "Norm inflation for equations of KdV type with fractional dispersion." Differential Integral Equations 31 (11/12) 833 - 850, November/December 2018. https://doi.org/10.57262/die/1537840871