We present recent results on probabilistic well-posedness of the two dimensional NLS, posed on the sphere. These results deal with low regularity solutions. The construction of such solutions is beyond the scope of applicability of the deterministic methods of Burq-Gérard-Tzvetkov developed between 2000 and 2004.
Nicolas Burq 1 , 2 ; Nicolas Camps 3 ; Chenmin Sun 4 ; Nikolay Tzvetkov 5 , 2
Nicolas Burq; Nicolas Camps; Chenmin Sun; Nikolay Tzvetkov. Probabilistic well-posedness and Gibbs measure evolution for the non linear Schrödinger equation on the two dimensional sphere. Journées équations aux dérivées partielles (2025), Exposé no. 9, 9 p.. doi: 10.5802/jedp.700
@incollection{JEDP_2025____A9_0,
author = {Nicolas Burq and Nicolas Camps and Chenmin Sun and Nikolay Tzvetkov},
title = {Probabilistic well-posedness and {Gibbs} measure evolution for the non linear {Schr\"odinger} equation on the two dimensional sphere},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
note = {talk:9},
pages = {1--9},
year = {2025},
publisher = {R\'eseau th\'ematique AEDP du CNRS},
doi = {10.5802/jedp.700},
language = {en},
url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.700/}
}
TY - JOUR AU - Nicolas Burq AU - Nicolas Camps AU - Chenmin Sun AU - Nikolay Tzvetkov TI - Probabilistic well-posedness and Gibbs measure evolution for the non linear Schrödinger equation on the two dimensional sphere JO - Journées équations aux dérivées partielles N1 - talk:9 PY - 2025 SP - 1 EP - 9 PB - Réseau thématique AEDP du CNRS UR - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.700/ DO - 10.5802/jedp.700 LA - en ID - JEDP_2025____A9_0 ER -
%0 Journal Article %A Nicolas Burq %A Nicolas Camps %A Chenmin Sun %A Nikolay Tzvetkov %T Probabilistic well-posedness and Gibbs measure evolution for the non linear Schrödinger equation on the two dimensional sphere %J Journées équations aux dérivées partielles %Z talk:9 %D 2025 %P 1-9 %I Réseau thématique AEDP du CNRS %U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.700/ %R 10.5802/jedp.700 %G en %F JEDP_2025____A9_0
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