Abstract
The $I$-method in its first version as developed by Colliander et~al. in [2] is applied to prove that the Cauchy-problem for the generalized Korteweg-de Vries equation of order three (gKdV-3) is globally well-posed for large real-valued data in the Sobolev space $H^s(\mathbb R \rightarrow \mathbb R)$, provided $s>-\frac{1}{42}$.
Citation
Axel Grünrock. Mahendra Panthee. Jorge Drumond Silva. "A remark on global well-posedness below $L^2$ for the GKDV-3 equation." Differential Integral Equations 20 (11) 1229 - 1236, 2007. https://doi.org/10.57262/die/1356039286
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