Transport of gaussian measures by the flow of the nonlinear Schr\'odinger equation

Autor:	Planchon, F., Tzvetkov, N., Visciglia, N.
Rok vydání:	2018
Předmět:	Mathematics - Analysis of PDEs Mathematical Physics
Zdroj:	Math. Ann. 378 (2020), no. 1-2, 389-423
Druh dokumentu:	Working Paper
DOI:	10.1007/s00208-019-01879-4
Popis:	We prove a new smoothing type property for solutions of the 1d quintic Schr\"odinger equation. As a consequence, we prove that a family of natural gaussian measures are quasi-invariant under the flow of this equation. In the defocusing case, we prove global in time quasi-invariance while in the focusing case because of a blow-up obstruction we only get local in time quasi-invariance. Our results extend as well to generic odd power nonlinearities. Comment: Presentation improved
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1810.00526 Zobrazit plný text záznamu View this record from Arxiv