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New trends in ensemble forecast strategy: uncertainty quantification for coarse-grid computational fluid dynamics
Numerical simulations of industrial and geophysical fluid flows cannot usually solve the
exact Navier–Stokes equations. Accordingly, they encompass strong local errors. For some …
exact Navier–Stokes equations. Accordingly, they encompass strong local errors. For some …
[ספר][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 …
Numerically modeling stochastic Lie transport in fluid dynamics
We present a numerical investigation of stochastic transport in ideal fluids. According to
Holm [Proc. A, 471 (2015)] and Cotter, Gottwald, and Holm [Proc. A, 473 (2017)], the …
Holm [Proc. A, 471 (2015)] and Cotter, Gottwald, and Holm [Proc. A, 473 (2017)], the …
From additive to transport noise in 2d fluid dynamics
Abstract Additive noise in Partial Differential equations, in particular those of fluid
mechanics, has relatively natural motivations. The aim of this work is showing that suitable …
mechanics, has relatively natural motivations. The aim of this work is showing that suitable …
Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise
We construct Hölder continuous, global-in-time probabilistically strong solutions to 3D Euler
equations perturbed by Stratonovich transport noise. Kinetic energy of the solutions can be …
equations perturbed by Stratonovich transport noise. Kinetic energy of the solutions can be …
Sharp nonuniqueness of solutions to stochastic Navier–Stokes equations
In this paper we establish a sharp nonuniqueness result for stochastic-dimensional ()
incompressible Navier–Stokes equations. First, for every divergence-free initial condition in …
incompressible Navier–Stokes equations. First, for every divergence-free initial condition in …
Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier–Stokes equations
We consider a family of stochastic 2D Euler equations in vorticity form on the torus, with
transport-type noises and L^ 2 L 2-initial data. Under a suitable scaling of the noises, we …
transport-type noises and L^ 2 L 2-initial data. Under a suitable scaling of the noises, we …
[HTML][HTML] Stochastic approaches to deterministic fluid dynamics: a selective review
We present a stochastic Lagrangian view of fluid dynamics. The velocity solving the
deterministic Navier–Stokes equation is regarded as a mean time derivative taken over …
deterministic Navier–Stokes equation is regarded as a mean time derivative taken over …
A particle filter for stochastic advection by Lie transport: a case study for the damped and forced incompressible two-dimensional Euler equation
In this work, we combine a stochastic model reduction with a particle filter augmented with
tempering and jittering, and apply the combined algorithm to a damped and forced …
tempering and jittering, and apply the combined algorithm to a damped and forced …
Weak well-posedness by transport noise for a class of 2D fluid dynamics equations
A fundamental open problem in fluid dynamics is whether solutions to $2 $ D Euler
equations with $(L^ 1_x\cap L^ p_x) $-valued vorticity are unique, for some $ p\in [1,\infty) …
equations with $(L^ 1_x\cap L^ p_x) $-valued vorticity are unique, for some $ p\in [1,\infty) …