[کتاب][B] Stochastic partial differential equations in fluid mechanics

F Flandoli, E Luongo - 2023‏ - Springer
These notes originated from a series of lectures given at Waseda University in April–May
2021, supported by Top Global University Project of Waseda University. The first author …

Parameter recovery for the 2 dimensional Navier--Stokes equations via continuous data assimilation

E Carlson, J Hudson, A Larios - SIAM Journal on Scientific Computing, 2020‏ - SIAM
We study a continuous data assimilation algorithm proposed by Azouani, Olson, and Titi
(AOT) in the context of an unknown viscosity. We determine the large-time error between the …

Global in time stability and accuracy of IMEX-FEM data assimilation schemes for Navier–Stokes equations

A Larios, LG Rebholz, C Zerfas - Computer Methods in Applied Mechanics …, 2019‏ - Elsevier
We study numerical schemes for incompressible Navier–Stokes equations using IMEX
temporal discretizations, finite element spatial discretizations, and equipped with continuous …

Exponential mixing for a class of dissipative PDEs with bounded degenerate noise

S Kuksin, V Nersesyan, A Shirikyan - Geometric and Functional Analysis, 2020‏ - Springer
We study a class of discrete-time random dynamical systems with compact phase space.
Assuming that the deterministic counterpart of the system in question possesses a …

Well-posedness of the 3D stochastic primitive equations with multiplicative and transport noise

Z Brzeźniak, J Slavík - Journal of Differential Equations, 2021‏ - Elsevier
We show that the stochastic 3D primitive equations with the Neumann boundary condition
on the top, the lateral Dirichlet boundary condition and either the Dirichlet or the Neumann …

Generalized couplings and ergodic rates for SPDEs and other Markov models

O Butkovsky, A Kulik, M Scheutzow - The Annals of Applied Probability, 2020‏ - JSTOR
We establish verifiable general sufficient conditions for exponential or subexponential
ergodicity of Markov processes that may lack the strong Feller property. We apply the …

On unique ergodicity in nonlinear stochastic partial differential equations

N Glatt-Holtz, JC Mattingly, G Richards - Journal of Statistical Physics, 2017‏ - Springer
We illustrate how the notion of asymptotic coupling provides a flexible and intuitive
framework for proving the uniqueness of invariant measures for a variety of stochastic partial …

Super-Exponential Convergence Rate of a Nonlinear Continuous Data Assimilation Algorithm: The 2D Navier–Stokes Equation Paradigm

E Carlson, A Larios, ES Titi - Journal of Nonlinear Science, 2024‏ - Springer
We study a nonlinear-nudging modification of the Azouani–Olson–Titi continuous data
assimilation (downscaling) algorithm for the 2D incompressible Navier–Stokes equations …

Unique ergodicity for fractionally dissipated, stochastically forced 2D Euler equations

P Constantin, N Glatt-Holtz, V Vicol - Communications in Mathematical …, 2014‏ - Springer
Unique Ergodicity for Fractionally Dissipated, Stochastically Forced 2D Euler Equations Page 1
Digital Object Identifier (DOI) 10.1007/s00220-014-2003-3 Commun. Math. Phys. 330, 819–857 …

The stochastic primitive equations with transport noise and turbulent pressure

A Agresti, M Hieber, A Hussein, M Saal - Stochastics and Partial …, 2024‏ - Springer
In this paper we consider the stochastic primitive equation for geophysical flows subject to
transport noise and turbulent pressure. Admitting very rough noise terms, the global …