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Article Dans Une Revue Journal of Functional Analysis Année : 2021

Quasi-Invariance of Gaussian Measures Transported by the Cubic NLS with Third-Order Dispersion on T

Arnaud Debussche
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Yoshio Tsutsumi
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Résumé

We consider the Nonlinear Schrödinger (NLS) equation and prove that the Gaussian measure with covariance (1 − ∂ 2 x) −α on L 2 (T) is quasi-invariant for the associated flow for α > 1/2. This is sharp and improves a previous result obtained in [20] where the values α > 3/4 were obtained. Also, our method is completely different and simpler, it is based on an explicit formula for the Radon-Nikodym derivative. We obtain an explicit formula for this latter in the same spirit as in [4] and [5]. The arguments are general and can be used to other Hamiltonian equations.
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Dates et versions

hal-02477109 , version 1 (13-02-2020)

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Arnaud Debussche, Yoshio Tsutsumi. Quasi-Invariance of Gaussian Measures Transported by the Cubic NLS with Third-Order Dispersion on T. Journal of Functional Analysis, 2021, 281 (3), pp.article n° 109032. ⟨10.1016/j.jfa.2021.109032⟩. ⟨hal-02477109⟩
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