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Uniqueness for an inviscid stochastic dyadic model on a tree. (English) Zbl 1329.60207
Summary: 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 proved using a technique relying on the properties of the \(q\)-matrix associated to a continuous-time Markov chain.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60J27 Continuous-time Markov processes on discrete state spaces
60J28 Applications of continuous-time Markov processes on discrete state spaces
35R60 PDEs with randomness, stochastic partial differential equations
35Q31 Euler equations
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
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