Ergodicity of the finite dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise [PDF]
arXiv, 2002 We prove ergodicity of the finite dimensional approximations of the three dimensional Navier-Stokes equations, driven by a random force. The forcing noise acts only on a few modes and some algebraic conditions on the forced modes are found that imply the ergodicity. The convergence rate to the unique invariant measure is shown to be exponential.
arxiv
Stochastic Navier-Stokes Equations on a Thin Spherical Domain. [PDF]
Appl Math Optim, 2021 Brzeźniak Z, Dhariwal G, Le Gia QT.
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Smooth or singular solutions to the Navier--Stokes system ? [PDF]
arXiv, 2002 The existence of singular solutions of the incompressible Navier-Stokes system with singular external forces, the existence of regular solutions for more regular forces as well as the asymptotic stability of small solutions (including stationary ones), and a pointwise loss of smoothness for solutions are proved in the same function space of ...
arxiv
A probabilistic representation for the vorticity of a 3D viscous fluid and for general systems of parabolic equations [PDF]
arXiv, 2003 A probabilistic representation formula for general systems of linear parabolic equations, coupled only through the zero-order term, is given. On this basis, an implicit probabilistic representation for the vorticity in a 3D viscous fluid (described by the Navier-Stokes equations) is carefully analysed, and a theorem of local existence and uniqueness is
arxiv
Note on the finite time singularities for the 3D Navier-Stokes equations [PDF]
arXiv, 2005 The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.
arxiv
Regularity of transition semigroups associated to a 3D stochastic Navier-Stokes equation [PDF]
arXiv, 2006 A 3D stochastic Navier-Stokes equation with a suitable non degenerate additive noise is considered. The regularity in the initial conditions of every Markov transition kernel associated to the equation is studied by a simple direct approach. A by-product of the technique is the equivalence of all transition probabilities associated to every Markov ...
arxiv
Existence of martingale and stationary suitable weak solutions for a stochastic Navier-Stokes system [PDF]
arXiv, 2006 The existence of suitable weak solutions of 3D Navier-Stokes equations, driven by a random body force, is proved. These solutions satisfy a local balance of energy. Moreover it is proved also the existence of a statistically stationary solution.
arxiv
A regularity criterion for the Navier-Stokes equations in terms of the pressure gradient
Open Mathematics, 2014 Bosia Stefano +2 more
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2D Smagorinsky type large eddy models as limits of stochastic PDEs
, 2023 Flandoli F, Luo D, Luongo E.
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An optimal adaptive wavelet method for first order system least squares. [PDF]
Numer Math (Heidelb), 2018 Rekatsinas N, Stevenson R.
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