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arXiv · 1810.00526

Transport of gaussian measures by the flow of the nonlinear Schrödinger equation

F. Planchon·N. Tzvetkov·N. Visciglia
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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.

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F. Planchon, N. Tzvetkov, N. Visciglia. 2019-07-21. Transport of gaussian measures by the flow of the nonlinear Schrödinger equation. https://doi.org/10.1007/s00208-019-01879-4

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