Stochastic Navier-Stokes Equations for Turbulent Flows

By R. Mikulevicius, Boris L. Rozovskii. SIAM Journal on Mathematical Analysis, 2004

333 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics, Finance

View Paper: https://www.semanticscholar.org/paper/bb40ad52d21aa92cd99fee468dcf467627c7687f

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Citations in the corpus

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.”
An Introduction to 3D Stochastic Fluid Dynamics (2008, neutral): “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]).”
Stochastic Volterra Equations in Banach Spaces and Stochastic Partial Differential Equations (2008, methodology): “[49] R. Mikulevicius and B.L. Rozovskii: Stochastic Navier-Stokes equations for turbulent flows.”
Strong pathwise solutions of the stochastic Navier-Stokes system (2009, methodology): “[25] R. Mikulevicius and B. L. Rozovskii, Global L2-solutions of stochastic Navier-Stokes equations, Ann.”
Large Deviations for Stochastic Tamed 3D Navier-Stokes Equations (2010, methodology): “[ 16 , 26]). Moreover, without the term gN ,t he existence and ergodicity of invariant measures for (1) have already been studied by using Kolmogorov operators (cf.”
Global L2-solutions of stochastic Navier–Stokes equations (2005, methodology): “in [25], [ 28 ] suggests the following form of this equation for the unknown functions u= i ul ¢ 1•l•d ; p; ~ p :”
Local martingale and pathwise solutions for an abstract fluids model (2010, neutral): “See [5, 2, 6, 33].”
On the existence and uniqueness of solutions to stochastic three-dimensional Lagrangian averaged Navier–Stokes equations (2006, background): “Later, this approach was substantially developed and extended by many authors (see, e.g. Mikulevicius & Rozovskii (2004, 2005) and the references therein).”
Wellposedness for stochastic continuity equations with Ladyzhenskaya–Prodi–Serrin condition (2013, background): “The reader is further addressed to Flandoli [12], Mikulevicius, Rozovskii [22], and references therein.”
Parameter estimation for the stochastically perturbed Navier-Stokes equations (2010, neutral): “See, for instance, [2, 3, 4, 7, 12, 13, 30] and containing references.”
A theory of regularity structures (2013, background): “For example, the case of the stochastic Navier–Stokes equations has been considered in [85], while the case of a stochastic version of the nonlinear heat equation was considered in [7].”
Stochastic Differential Equations: A Wiener Chaos Approach (2005, neutral): “Most of the results of this section come from the two papers [35] and [31].”