Partial regularity for the stochastic Navier-Stokes equations

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Local martingale and pathwise solutions for an abstract fluids model (2010, methodology): “with our methods. 1 2 A.Debussche,N.Glatt-HoltzandR.Temam Let us recall at this point that the theory of the related stochastic Navier-Stokesequations haveundergone substantial developments; see e.g. [3, 48, 9, 8, 17, 12, 2, 5, 6, 19, 10, 36, 37, 45, 18, 23]. However to emphasizethe notable diﬀerenc”
An Introduction to 3D Stochastic Fluid Dynamics (2008, methodology): “Weinan E and Mattingly [27] in d = 2 and Romito [59] in d = 3 proved that ergodicity is true if the noise is active at least on a very small number of modes (like 4), properly displaced to “generate” all other modes through the action of the drift.”
Ergodicity Results for the Stochastic Navier–Stokes Equations: An Introduction (2013, background): “Existence and uniqueness have been studied in various articles (se for instance [1], [3], [4], [5], [9], [10], [11], [13], [15], [21], [30], [32], [51], [53], [54], [68], [69]) and this part of the theory is well understood.”
Markov selections for the 3D stochastic Navier–Stokes equations (2006, background): “regularity of paths at any given time (see [18] for an example).”