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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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