DG-MP-PDE Seminar: Mass critical generalized KdV equation

I will discuss the scattering problem of mass-critical generalized KdV equation. We will see if the scattering of gKdV fails, then a minimal mass blow-up solution exist on the condition that scattering of mass-critical 1D NLS is true. We use concentration compactness argument in addition to an observation that a certain modulated, rescaled version of NLS solution is approximately gKdV solution for highly oscillatory profile.