The Annals of Applied Probability

Anomalous dissipation in a stochastic inviscid dyadic model

David Barbato, Franco Flandoli, and Francesco Morandin

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A stochastic version of an inviscid dyadic model of turbulence, with multiplicative noise, is proved to exhibit energy dissipation in spite of the formal energy conservation. As a consequence, global regular solutions cannot exist. After some reductions, the main tool is the escape bahavior at infinity of a certain birth and death process.

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Ann. Appl. Probab., Volume 21, Number 6 (2011), 2424-2446.

First available in Project Euclid: 23 November 2011

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Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 60J28: Applications of continuous-time Markov processes on discrete state spaces 35B65: Smoothness and regularity of solutions 76B03: Existence, uniqueness, and regularity theory [See also 35Q35]

SPDE shell models dyadic model fluid dynamics anomalous dissipation blow-up Girsanov’s transform multiplicative noise


Barbato, David; Flandoli, Franco; Morandin, Francesco. Anomalous dissipation in a stochastic inviscid dyadic model. Ann. Appl. Probab. 21 (2011), no. 6, 2424--2446. doi:10.1214/11-AAP768.

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