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Pré-Publication, Document De Travail Année : 2023

Noninvariance of Gaussian Measures Under the 2D Euler Flow

Résumé

In this article we consider the two-dimensional incompressible Euler equations and give a sufficient condition on Gaussian measures of jointly independent Fourier coefficients supported on H^σ (T^2) (σ > 3) such that these measures are not invariant (in vorticity form). We show that this condition holds on an open and dense set in suitable topologies (and so is generic in a Baire category sense) and give some explicit examples of Gaussian measures which are not invariant. We also pose a few related conjectures which we believe to be approachable.
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hal-04196556 , version 1 (05-09-2023)

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  • HAL Id : hal-04196556 , version 1

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Jacob Bedrossian, Mickaël Latocca. Noninvariance of Gaussian Measures Under the 2D Euler Flow. 2023. ⟨hal-04196556⟩
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