The aim of these notes is to provide a brief overview of a large body recent work whose aim was to prove the Threshold Theorem for energy critical geometric nonlinear wave equations. Within the class of geometric wave equations we include nonlinear wave evolutions which have a geometric structure and origin, including a nontrivial gauge group. The problems discussed here include Wave Maps, Maxwell–Klein–Gordon, as well as the hyperbolic Yang–Mills flow. In a nutshell, the Threshold theorem asserts that these problems are globally well-posed for initial data below the ground state energy.
@incollection{JEDP_2018____A10_0,
author = {Daniel Tataru},
title = {The threshold theorem for geometric nonlinear wave equations},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
note = {talk:10},
pages = {1--15},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2018},
doi = {10.5802/jedp.670},
language = {en},
url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.670/}
}
TY - JOUR AU - Daniel Tataru TI - The threshold theorem for geometric nonlinear wave equations JO - Journées équations aux dérivées partielles N1 - talk:10 PY - 2018 SP - 1 EP - 15 PB - Groupement de recherche 2434 du CNRS UR - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.670/ DO - 10.5802/jedp.670 LA - en ID - JEDP_2018____A10_0 ER -
%0 Journal Article %A Daniel Tataru %T The threshold theorem for geometric nonlinear wave equations %J Journées équations aux dérivées partielles %Z talk:10 %D 2018 %P 1-15 %I Groupement de recherche 2434 du CNRS %U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.670/ %R 10.5802/jedp.670 %G en %F JEDP_2018____A10_0
Daniel Tataru. The threshold theorem for geometric nonlinear wave equations. Journées équations aux dérivées partielles (2018), Exposé no. 10, 15 p. doi : 10.5802/jedp.670. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.670/
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