We construct time quasi-periodic solutions and prove almost global existence for the energy supercritical nonlinear Schrödinger equations on the torus in arbitrary dimensions. The main new ingredient is a geometric selection in the Fourier space. This method is applicable to other nonlinear equations.
@article{SEDP_2009-2010____A32_0,
author = {Wang, Wei-Min},
title = {Supercritical nonlinear {Schr\"odinger} equations: {Quasi-periodic} solutions and almost global existence},
journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
note = {talk:32},
pages = {1--18},
publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2009-2010},
language = {en},
url = {http://www.numdam.org/item/SEDP_2009-2010____A32_0/}
}
TY - JOUR AU - Wang, Wei-Min TI - Supercritical nonlinear Schrödinger equations: Quasi-periodic solutions and almost global existence JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:32 PY - 2009-2010 SP - 1 EP - 18 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/item/SEDP_2009-2010____A32_0/ LA - en ID - SEDP_2009-2010____A32_0 ER -
%0 Journal Article %A Wang, Wei-Min %T Supercritical nonlinear Schrödinger equations: Quasi-periodic solutions and almost global existence %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:32 %D 2009-2010 %P 1-18 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/item/SEDP_2009-2010____A32_0/ %G en %F SEDP_2009-2010____A32_0
Wang, Wei-Min. Supercritical nonlinear Schrödinger equations: Quasi-periodic solutions and almost global existence. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2009-2010), Exposé no. 32, 18 p. http://www.numdam.org/item/SEDP_2009-2010____A32_0/
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