Nous considérons dans cet article l’équation des ondes semilinéaire critique
posée dans tout l’espace , avec Shatah et Struwe [31] ont prouvé que si les données initiales sont d’énergie finie, c’est à dire si , alors il existe une solution globale. Planchon [22] a montré que c’est aussi le cas pour certaines données initiales d’énergie infinie : il suffit que les données initiales soient de norme petite dans . Nous construisons ici des solutions globales de pour des données initiales d’énergie infinie arbitrairement grandes, en utilisant deux méthodes qui reviennent à interpoler entre solutions d’énergie finie et solutions d’énergie infinie : la méthode de Bourgain et la méthode de Calderón. Ces deux méthodes donnent des résultats complémentaires.
@article{SEDP_2006-2007____A11_0, author = {Germain, Pierre}, title = {Solutions globales d{\textquoteright}\'energie infinie pour l{\textquoteright}\'equation des ondes critique}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:11}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2006-2007}, mrnumber = {2385198}, language = {fr}, url = {http://www.numdam.org/item/SEDP_2006-2007____A11_0/} }
TY - JOUR AU - Germain, Pierre TI - Solutions globales d’énergie infinie pour l’équation des ondes critique JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:11 PY - 2006-2007 DA - 2006-2007/// PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/item/SEDP_2006-2007____A11_0/ UR - https://www.ams.org/mathscinet-getitem?mr=2385198 LA - fr ID - SEDP_2006-2007____A11_0 ER -
Germain, Pierre. Solutions globales d’énergie infinie pour l’équation des ondes critique. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2006-2007), Exposé no. 11, 31 p. http://www.numdam.org/item/SEDP_2006-2007____A11_0/
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