Uniqueness and blow-up for the noisy viscous dyadic model

2011/11/02 by Marco Romito, Romito, Marco
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 76D03 #Probability (math.PR) #Secondary 35Q35 60H15 35R60 #math.AP #math.PR #msc:35Q35 #msc:35R60 #msc:60H15 #msc:76D03

paper · pdf · doi:10.48550/arxiv.1111.0536

39 pages

arxiv created 2011/11/02 · arxiv updated 2011/11/03

Abstract

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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