Abstract
In this paper, we adapt and extend B. Birnir, G. Ponce, and N. Svanstedt result related with local ill-posedness for the Cauchy problem to the mKdV equation in [5] to the generalized $p$-Gardner equation. We prove that the Cauchy problem for the generalized $2$-Gardner equation is ill-posed in the Sobolev space $H^s(\mathbb{R})$ for $s < -\frac12$.
Citation
Gilberto Arenas-Díaz. José R. Quintero. "On the local ill-posedness of the generalized $p$-Gardner equation." Differential Integral Equations 27 (11/12) 1025 - 1036, November/December 2014. https://doi.org/10.57262/die/1408366783
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