Two blow-up regimes for $L^2$ supercritical nonlinear Schrödinger equations

Merle, Frank; Raphaël, Pierre; Szeftel, Jérémie

Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2009-2010), Exposé no. 2, 11 p.

We consider the focusing nonlinear Schrödinger equations $i{\partial }_{t}u+\Delta u+u{\left|u\right|}^{p-1}=0$. We prove the existence of two finite time blow up dynamics in the supercritical case and provide for each a qualitative description of the singularity formation near the blow up time.

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