On mass concentration for the critical generalized Korteweg-de Vries equation

We show that blow-up solutions of the critical generalized Korteweg–de Vries equation in $H^{1}(\mathbb{R})$ concentrate at least the mass of the ground state at the blow-up time. The I-method is used to prove a slightly weaker result in $H^{s}(\mathbb{R})$ with $16/17 < s < 1$. Under an assumption on the precise blow-up rate, we are able to use similar arguments to prove a more precise analogue of the $H^{1}(\mathbb{R})$ concentration result over the same range of $s$.

Link to Journal

B. Pigott, "On mass concentration for the critical generalized Korteweg-de Vries equation." Proc. Edinb. Math. Soc. (2). 59 (2) (2016).