Resumen de On continuation properties after blow-up time for L2-critical gKdV equations

Yang Lan

• In this paper, we consider a blow-up solution u(t) (close to the soliton manifold) to the L2-critical gKdV equation ∂tu+(uxx+u5)x=0, with finite blow-up time T<+∞. We expect to construct a natural extension of u(t) after the blow-up time. To do this, we consider the solution uγ(t) to the saturated L2-critical gKdV equation ∂tu+(uxx+u5−γu|u|q−1)x=0 with the same initial data, where γ>0 and q>5. A standard argument shows that uγ(t) is always global in time. Moreover, for all t