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

Frank Merle[1]; Pierre Raphaël[2]; Jérémie Szeftel[3]

  • [1] Université de Cergy Pontoise and IHES France
  • [2] IMT Université Paul Sabatier Toulouse France
  • [3] DMA Ecole Normale Supérieure France

Séminaire Équations aux dérivées partielles (2009-2010)

  • Volume: 2009-2010, page 1-11

Abstract

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We consider the focusing nonlinear Schrödinger equations i ∂ t u + Δ 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.

How to cite

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Merle, Frank, Raphaël, Pierre, and Szeftel, Jérémie. "Two blow-up regimes for $L^2$ supercritical nonlinear Schrödinger equations." Séminaire Équations aux dérivées partielles 2009-2010 (2009-2010): 1-11. <http://eudml.org/doc/116445>.

@article{Merle2009-2010,
abstract = {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.},
affiliation = {Université de Cergy Pontoise and IHES France; IMT Université Paul Sabatier Toulouse France; DMA Ecole Normale Supérieure France},
author = {Merle, Frank, Raphaël, Pierre, Szeftel, Jérémie},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {nonlinear Schrödinger equations; self-similar blow-up; log-log blow-up},
language = {eng},
pages = {1-11},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Two blow-up regimes for $L^2$ supercritical nonlinear Schrödinger equations},
url = {http://eudml.org/doc/116445},
volume = {2009-2010},
year = {2009-2010},
}

TY - JOUR
AU - Merle, Frank
AU - Raphaël, Pierre
AU - Szeftel, Jérémie
TI - Two blow-up regimes for $L^2$ supercritical nonlinear Schrödinger equations
JO - Séminaire Équations aux dérivées partielles
PY - 2009-2010
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2009-2010
SP - 1
EP - 11
AB - 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.
LA - eng
KW - nonlinear Schrödinger equations; self-similar blow-up; log-log blow-up
UR - http://eudml.org/doc/116445
ER -

References

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