Two blow-up regimes for ${L}^{2}$ supercritical nonlinear Schrödinger equations
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 $i{\partial }_{t}u+\Delta u+u{|u|}^{p-1}=0$. 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.

@article{SEDP_2009-2010____A2_0,
author = {Merle, Frank and Rapha\"el, Pierre and Szeftel, J\'er\'emie},
title = {Two blow-up regimes for $L^2$ supercritical nonlinear {Schr\"odinger} equations},
journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
note = {talk:2},
publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2009-2010},
language = {en},
url = {http://www.numdam.org/item/SEDP_2009-2010____A2_0/}
}
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Merle, Frank; Raphaël, Pierre; Szeftel, Jérémie. Two blow-up regimes for $L^2$ supercritical nonlinear Schrödinger equations. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2009-2010), Exposé no. 2, 11 p. http://www.numdam.org/item/SEDP_2009-2010____A2_0/

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