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[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 …
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
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 …
(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
We study numerical schemes for incompressible Navier–Stokes equations using IMEX
temporal discretizations, finite element spatial discretizations, and equipped with continuous …
temporal discretizations, finite element spatial discretizations, and equipped with continuous …
Exponential mixing for a class of dissipative PDEs with bounded degenerate noise
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 …
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
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 …
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
We establish verifiable general sufficient conditions for exponential or subexponential
ergodicity of Markov processes that may lack the strong Feller property. We apply the …
ergodicity of Markov processes that may lack the strong Feller property. We apply the …
On unique ergodicity in nonlinear stochastic partial differential equations
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 …
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
We study a nonlinear-nudging modification of the Azouani–Olson–Titi continuous data
assimilation (downscaling) algorithm for the 2D incompressible Navier–Stokes equations …
assimilation (downscaling) algorithm for the 2D incompressible Navier–Stokes equations …
Unique ergodicity for fractionally dissipated, stochastically forced 2D Euler equations
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 …
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
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 …
transport noise and turbulent pressure. Admitting very rough noise terms, the global …