Dans cette Note, nous démontrons un résultat dʼexplosion en temps fini pour lʼéquation de Schrödinger non linéaire sur le tore avec une non linéarité du type , . En particulier, notre résultat dʼexplosion est vrai pour des puissances p plus grandes que lʼexposant de Strauss. Cette situation est contraire au cas non périodique où lʼon connaît que pour p supérieur à lʼexposant de Strauss, le problème de Cauchy est globalement bien posé.
In this Note, we prove a finite-time blowup result for the periodic nonlinear Schrödinger equation on with nonlinearity for . In particular, our blowup result holds above the Strauss exponent. This is in contrast with the non-periodic setting, where global existence for small data is known above the Strauss exponent.
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@article{CRMATH_2012__350_7-8_389_0, author = {Oh, Tadahiro}, title = {A blowup result for the periodic {NLS} without gauge invariance}, journal = {Comptes Rendus. Math\'ematique}, pages = {389--392}, publisher = {Elsevier}, volume = {350}, number = {7-8}, year = {2012}, doi = {10.1016/j.crma.2012.04.009}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2012.04.009/} }
TY - JOUR AU - Oh, Tadahiro TI - A blowup result for the periodic NLS without gauge invariance JO - Comptes Rendus. Mathématique PY - 2012 SP - 389 EP - 392 VL - 350 IS - 7-8 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2012.04.009/ DO - 10.1016/j.crma.2012.04.009 LA - en ID - CRMATH_2012__350_7-8_389_0 ER -
%0 Journal Article %A Oh, Tadahiro %T A blowup result for the periodic NLS without gauge invariance %J Comptes Rendus. Mathématique %D 2012 %P 389-392 %V 350 %N 7-8 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2012.04.009/ %R 10.1016/j.crma.2012.04.009 %G en %F CRMATH_2012__350_7-8_389_0
Oh, Tadahiro. A blowup result for the periodic NLS without gauge invariance. Comptes Rendus. Mathématique, Tome 350 (2012) no. 7-8, pp. 389-392. doi : 10.1016/j.crma.2012.04.009. http://archive.numdam.org/articles/10.1016/j.crma.2012.04.009/
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