For the L2-critical generalized KdV equation, blow-up is not possible for subcritical mass elements. A minimal mass blow-up exists, as does a description of the flow for slightly supercritical mass elements. For such initial data, a finite-time blow-up occurs with

\( \|u_x\|_{L^2}\sim(T-t)^{-\nu} \)

where \( \nu \) is the blow-up rate. We will focus on results concerning finite-time infinite-point blow-up, which occurs for \( \nu \geq 1/2 \). Previously, the blow-up rate of such solutions was limited with a lower bound of 11/13; in my previous work, this has been improved to 1/2 strictly.
This year I’ve constructed solutions with the blow up rate of 1/2. This rate is in the transition between infinite and finite point blow up, and corresponds to slow blow up. We will discuss the construction of such solutions and their instability.