The Annals of Applied Probability

Anomalous dissipation in a stochastic inviscid dyadic model

David Barbato, Franco Flandoli, and Francesco Morandin

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 23 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1322057326

Digital Object Identifier
doi:10.1214/11-AAP768

Mathematical Reviews number (MathSciNet)
MR2895420

Zentralblatt MATH identifier
1259.60064

Subjects
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]

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

Citation

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. https://projecteuclid.org/euclid.aoap/1322057326


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