An Introduction to 3D Stochastic Fluid Dynamics

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Ergodicity Results for the Stochastic Navier–Stokes Equations: An Introduction (2013, background): “2) and weak-strong uniqueness (see [29]) which guaranty that if a strong exists then every weak solution is equal to this strong solution.”
Local martingale and pathwise solutions for an abstract fluids model (2010, unknown): “See, for example, [15] for further details.”
Fluid flow dynamics under location uncertainty (2013, background): “As initiated by (Bensoussan and Temam 1973) and intensively studied by many authors, since then (see for instance the review Flandoli 2008, and references therein) such a formalization has been mainly considered through the addition of random forcing terms to a standard expression of Navier-Stokes…”
Splitting up method for the 2D stochastic Navier–Stokes equations (2013, background): “For a comprehensive setting and higher dimension, we refer to [12] and the references therein.”
Well-posedness of stochastic partial differential equations with Lyapunov condition (2013, background): “[10,20,39]), the uniqueness and regularity of weak solutions are still open problems up to now.”