Ergodicity for the 3D stochastic Navier–Stokes equations

By Giuseppe Da Prato, Arnaud Debussche. 2003

213 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Finance

View Paper: https://www.semanticscholar.org/paper/41d9cf9855ba1f96823366732c0c36c6a5d2d585

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Citations in the corpus

2D Stochastic Navier–Stokes Equations with a Time-Periodic Forcing Term (2008, background): “Also in the 3D case, there has been a lot of recent progress ([6], [9], [13], [16], [25], [26]).”
Elliptic and parabolic equations for measures (2009, background): “, the book [67]), especially connected with stochastic partial differential equations (see [11], [52], [57], [58], [62], [63], [70], [74], [79], [82], [90], [91], [128], [150], [163]), infinite gradient systems, Gibbs measures, and stochastic quantization (see [5], [6], [56], [83], [85], [86], [96],”
On Ill‐ and Well‐Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations (2020, methodology): “as shown by Glatt-Holtz and Vicol [GHV14] and Ro¨ckner, Zhu and Zhu [RZZ14], respectively. Noise also has a beneﬁcial impact when it comes to long time behavior and ergodicity. Da Prato and Debussche [DPD03] obtained a unique ergodicity for three dimensional stochastic Navier–Stokes equations with n”
Ergodicity Results for the Stochastic Navier–Stokes Equations: An Introduction (2013, background): “It was also shown that, if the noise satisfies the assumptions of [16], the transition property hold for all time and similar properties as in [16] hold.”
Stochastic tamed 3D Navier–Stokes equations: existence, uniqueness and ergodicity (2008, background): “Recently, in [4, 5, 25], Da-Prato, Debussche and Odasso proved the existence and ergodicity of Markov solutions for 3D SNSE without the taming term gN , which are obtained as limits of Galerkin’s approximations.”
Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier–Stokes equations: Existence and nonuniqueness (2021, methodology): “However, the probabilistic counterpart, i.e. the Feller property and even the strong Feller property which corresponds to a smoothing with respect to the initial condition, was established for a sufficiently non-degenerate noise by Da Prato and Debussche [DPD03] and by Flandoli and Romito [FR08].”
Large Deviations for Stochastic Tamed 3D Navier-Stokes Equations (2010, background): “[1, 8, 9]) and the existence of Markovian selections (cf.”
Global L2-solutions of stochastic Navier–Stokes equations (2005, background): “ess) of a strong (pathwise) solution of the related Navier–Stokes equation. The existence and uniqueness of L 2-solutions of stochastic Navier–Stokes equations was studied by many authors (see, e.g., [2, 5, 6, 8, 9, 10, 11, 12, 25, 28, 33, 34, 35, 36]). There is also substantial literature on more r”
Exponential mixing for stochastic PDEs: the non-additive case (2005, background): “Another topic of interest is to try to prove exponential mixing in the three dimensional case for the transition semigroup constructed in [5].”
An Introduction to 3D Stochastic Fluid Dynamics (2008, methodology): “The theory in the 2D case is richer of well posedness results, even for cylindrical noise, ergodicity, control, non-viscous case and limit, see among others references [2], [3], [4], [6], [8], [9], [11], [13], [14], [17], [21], [22], [ 23 ], [28], [30], [31], [32], [47], [49], [50], [51], [55], [56]”
Local and global well-posedness of SPDE with generalized coercivity conditions☆ (2012, background): “[31, 13, 24] and the references therein), the results for the three dimensional case are still quite incomplete due to the lack of uniqueness (cf.[11, 12, 15, 16, 19, 20, 33, 34]).”
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”