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arXiv · 1508.00824

Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schr\"odinger equation

Tadahiro Oh·Nikolay Tzvetkov
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Abstract

We consider the cubic fourth order nonlinear Schr\"odinger equation on the circle. In particular, we prove that the mean-zero Gaussian measures on Sobolev spaces $H^s(\mathbb{T})$, $s > \frac34$, are quasi-invariant under the flow.

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Tadahiro Oh, Nikolay Tzvetkov. 2015-08-04. Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schr\"odinger equation. https://arxiv.org/abs/1508.00824

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