We analyze Runge--Kutta (RK) implicit-explicit (IMEX) time-stepping schemes to approximate the Cauchy problem associated with a partial differential equation of convection-diffusion-type, i.e., comprising a first-order part (the transport operator) and a second-order part (the diffusion operator). The proposed approach departs

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