Size of data in implicit function problems and singular perturbations for nonlinear Schr\'odinger systems

Autor:	Baldi, Pietro, Haus, Emanuele
Rok vydání:	2019
Předmět:	Mathematics - Analysis of PDEs Mathematics - Functional Analysis 47J07 35B25 35Q55 35G55
Druh dokumentu:	Working Paper
Popis:	We investigate a general question about the size and regularity of the data and the solutions in implicit function problems with loss of regularity. First, we give a heuristic explanation of the fact that the optimal data size found by Ekeland and S\'er\'e with their recent non-quadratic version of the Nash-Moser theorem can also be recovered, for a large class of nonlinear problems, with quadratic schemes. Then we prove that this heuristic observation applies to the singular perturbation Cauchy problem for the nonlinear Schr\"odinger system studied by M\'etivier, Rauch, Texier, Zumbrun, Ekeland, S\'er\'e. Using a "free flow component" decomposition and applying an abstract Nash-Moser-H\"ormander theorem, we improve the existing results regarding both the size of the data and the regularity of the solutions. Comment: 36 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1906.12290 Zobrazit plný text záznamu View this record from Arxiv