Blow up for the critical gKdV equation. II: Minimal mass dynamics

Source abstract

We consider the mass critical (gKdV) equation u_t + (u_{xx} + u^5)_x =0 for initial data in H^1 . We first prove the existence and uniqueness in the energy space of a minimal mass blow up solution and give a sharp description of the corresponding blow up soliton-like bubble. We then show that this solution is the universal attractor of all solutions near the ground state which have a defocusing behavior. This allows us to sharpen the description of near soliton dynamics obtained in [29].