Uniqueness and blow-up for a stochastic viscous dyadic model |
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Authors: | Marco Romito |
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Affiliation: | 1. Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy
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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 pathwise 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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