Electronic Communications in Probability

Uniqueness for an inviscid stochastic dyadic model on a tree

Luigi Bianchi

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In this paper we prove that the lack of uniqueness for solutions of the tree dyadic model of turbulence is overcome with the introduction of a suitable noise. The uniqueness is a weak probabilistic uniqueness for all $l^2$-initial conditions and is proven using a technique relying on the properties of the   $q$-matrix associated to a continuous time Markov chain.

Article information

Electron. Commun. Probab., Volume 18 (2013), paper no. 8, 12 pp.

Accepted: 31 January 2013
First available in Project Euclid: 7 June 2016

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Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 35Q31: Euler equations [See also 76D05, 76D07, 76N10] 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 60J28: Applications of continuous-time Markov processes on discrete state spaces 76B03: Existence, uniqueness, and regularity theory [See also 35Q35]

SPDE shell models dyadic model tree dyadic model q-matrix fluid dynamics Girsanov’s transform multiplicative noise

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Bianchi, Luigi. Uniqueness for an inviscid stochastic dyadic model on a tree. Electron. Commun. Probab. 18 (2013), paper no. 8, 12 pp. doi:10.1214/ECP.v18-2382. https://projecteuclid.org/euclid.ecp/1465315547

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