Uniqueness and blow-up for the noisy viscous dyadic model

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

2011-11-02

arxiv.org/abs/1111.0536v1

Mathematics

Probability

39 pages

Scientific paper

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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