In this paper, we prove that there exist no blow-up solutions of the critical generalized Korteweg‒de Vries (gKdV) equation with minimal L2-mass, assuming an L2-decay on the right on the initial data.
"Nonexistence of blow-up solution with minimal L2-mass for the critical gKdV equation." Duke Math. J. 115 (2) 385 - 408, 1 November 2002. https://doi.org/10.1215/S0012-7094-02-11526-9