The b-Novikov equation exhibits norm inflation in H^{3/2}(R), establishing ill-posedness at the critical Sobolev index.
Rodr´ ıguez-Blanco,On the Cauchy problem for the Camassa-Holm equation, Nonlinear Anal.46(2001), no
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Ill-posedness in the critical Sobolev space for the $b$-Novikov equation
The b-Novikov equation exhibits norm inflation in H^{3/2}(R), establishing ill-posedness at the critical Sobolev index.