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 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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2018
- DOI:
- 10.48550/arXiv.1810.00526
- arXiv:
- arXiv:1810.00526
- Bibcode:
- 2018arXiv181000526P
- Keywords:
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- Mathematics - Analysis of PDEs;
- Mathematical Physics
- E-Print:
- Presentation improved