Dissipation Properties of Transport Noise in the Two-Layer Quasi-geostrophic Model

Carigi, Giulia; Luongo, Eliseo

doi:10.1007/s00021-023-00773-z

Cited by 7 publications

(3 citation statements)

References 17 publications

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“…Theorem 2. 16 The solutions { f n } n of (2.5) with initial data f 0 ∈ L 2 satisfy the Laplace principle on C 0 t H −s , with rate function I f 0 , uniformly on compact subsets of L 2 . In particular, they satisfy the LDP with the same rate function.…”

Section: ) Satisfy the Uniform Laplace Principle With The Rate Functionmentioning

confidence: 99%

“…In [40] we improved some of these results by providing quantitative convergence rates. Among recent related progresses let us finally mention [16] on a two-layer quasi-geostrophic model, [1,2] on reaction-diffusion equations, and [45] for a Smagorinsky type model where the additional viscous term has the form g(u) = ∇ • (g (u)∇u) for some g ∈ C 1 (R).…”

Section: Introductionmentioning

confidence: 99%

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LDP and CLT for SPDEs with transport noise

Galeati

Luo

2023

Stoch PDE: Anal Comp

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In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable scaling limit, to solution of the corresponding deterministic PDE with an additional viscosity term. Large deviations and Gaussian fluctuations underlying such scaling limit are investigated in two cases of interest: stochastic linear transport equations in dimension $$D\ge 2$$ D ≥ 2 and 2D Euler equations in vorticity form. In both cases, a central limit theorem with strong convergence and explicit rate is established. The proofs rely on nontrivial tools, like the solvability of transport equations with supercritical coefficients and $$\Gamma $$ Γ -convergence arguments.

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Section: ) Satisfy the Uniform Laplace Principle With The Rate Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

LDP and CLT for SPDEs with transport noise

Galeati

Luo

2023

Stoch PDE: Anal Comp

View full text Add to dashboard Cite

show abstract

“…Recently, a new stochastic approach has been developed in [13,14,18,12,16,10,6] to explain Boussinesq hypothesis that "turbulent fluctuations are dissipative on large scales" [5]. The idea, better explained below in Section 2, is that the large scales satisfy a Navier-Stokes type equation with a stochastic transport term corresponding to the action of small scales.…”

Section: Introductionmentioning

confidence: 99%