Blow-up dynamics in the mass super-critical NLS equations

We study stable blow-up dynamics in the L-2-supercritical nonlinear Schrodinger equation with radial symmetry in various dimensions. We first investigate the profile equation and extend the result of Wang (1990) and Budd et al. (1999) on the existence and local uniqueness of solutions of the cubic profile equation to other L-2-supercritical nonlinearities and dimensions d >= 2. We then numerically observe the multi-bump structure of such solutions, and in particular, exhibit the Q(1.0 )solution, a candidate for the stable blow-up profile. Next, using the dynamic rescaling method, we investigate stable blow-up solutions in the L-2-supercritical NLS and confirm the square root rate of the blow-up as well as the convergence of blow-up profiles to the Q(1.0) profile. (C) 2019 Elsevier B.V. All rights reserved.