Uniqueness and blow-up for the noisy viscous dyadic model
arXiv:1111.0536
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.
39 pages
References in corpus (4)
- Time--space white noise eliminates global solutions in reaction diffusion equations
- An almost sure energy inequality for Markov solutions to the 3D Navier-Stokes equations
- Conservative interacting particles system with anomalous rate of ergodicity
- Finite-time blowup and existence of global positive solutions of a semi-linear SPDE