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Continuity equation in LlogL for the 2D Euler equations under the enstrophy measure

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Abstract

The 2D Euler equations with random initial condition has been investigates by Albeverio and Cruzeiro (Commun Math Phys 129:431–444, 1990) and other authors. Here we prove existence of solutions for the associated continuity equation in Hilbert spaces, in a quite general class with LlogL densities with respect to the enstrophy measure.

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Acknowledgements

G. Da Prato and F. Flandoli are partially supported by GNAMPA from INDAM and by MIUR, PRIN projects 2015. M. Röckner is supported by CRC 1283 through the DFG.

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Authors and Affiliations

  1. Scuola Normale Superiore of Pisa, Pisa, Italy

    Giuseppe Da Prato & Franco Flandoli

  2. University of Bielefeld, Bielefeld, Germany

    Michael Röckner

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  1. Giuseppe Da Prato
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  2. Franco Flandoli
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  3. Michael Röckner
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Correspondence to Franco Flandoli.

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Da Prato, G., Flandoli, F. & Röckner, M. Continuity equation in LlogL for the 2D Euler equations under the enstrophy measure. Stoch PDE: Anal Comp 9, 491–509 (2021). https://doi.org/10.1007/s40072-020-00173-8

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  • DOI: https://doi.org/10.1007/s40072-020-00173-8

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