Transport of gaussian measures by the flow of the nonlinear Schrödinger equation
Abstract
We prove a new smoothing type property for solutions of the 1d quintic Schrödinger equation. As a consequence, we prove that a family of natural gaussian measures are quasiinvariant under the flow of this equation. In the defocusing case, we prove global in time quasiinvariance while in the focusing case because of a blowup obstruction we only get local in time quasiinvariance. Our results extend as well to generic odd power nonlinearities.
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 DOI:
 10.48550/arXiv.1810.00526
 arXiv:
 arXiv:1810.00526
 Bibcode:
 2018arXiv181000526P
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics
 EPrint:
 Presentation improved