# Uniqueness and blow-up for the noisy viscous dyadic model

@article{Romito2011UniquenessAB, title={Uniqueness and blow-up for the noisy viscous dyadic model}, author={Marco Romito}, journal={arXiv: Probability}, year={2011} }

We consider the dyadic model with viscosity and additive Gaussian noise as a simplified version of the stochastic Navier-Stokes equations, with the purpose of studying uniqueness and emergence of singularities. We prove path-wise uniqueness and absence of blow-up in the intermediate intensity of the non-linearity, morally corresponding to the 3D case, and blow-up for stronger intensity. Moreover, blow-up happens with probability one for regular initial data.

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