Large and Moderate Deviations Principles and Central Limit Theorem for the Stochastic 3D Primitive Equations with Gradient-Dependent Noise

Slavík, Jakub

doi:10.1007/s10959-021-01125-1

Cited by 6 publications

(5 citation statements)

References 38 publications

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“…martingale solutions whose regularity in space and time is the one of a weak solution, by an implicit Euler scheme is given in [24]. Large deviation principles [13] and moderate deviation principles [55] are known to hold for small multiplicative noise and short times [15]. The existence of a Markov selection is proven in [14] for additive noise.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Stochastic Primitive Equations with Horizontal Viscosity and Diffusivity

Saal¹,

Slavík²

2021

Preprint

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We establish the existence and uniqueness of pathwise strong solutions to the stochastic 3D primitive equations with only horizontal viscosity and diffusivity driven by transport noise on a cylindrical domain M = (−h, 0) × G, G ⊂ R 2 bounded and smooth, with the physical Dirichlet boundary conditions on the lateral part of the boundary. Compared to the deterministic case where the uniqueness of z-weak solutions holds in L 2 , more regular initial data are necessary to establish uniqueness in the anisotropic space H 1 z L 2 xy so that the existence of local pathwise solutions can be deduced from the Gyöngy-Krylov theorem. Global existence is established using the logarithmic Sobolev embedding, the stochastic Gronwall lemma and an iterated stopping time argument.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Stochastic Primitive Equations with Horizontal Viscosity and Diffusivity

Saal¹,

Slavík²

2021

Preprint

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“…[DZZ17]) and small times (see e.g. [DZ18]), for an extension to transport noise and moderate deviation principles see [Sla21]. The existence of a Markov selection is proven in [DZ17] for additive noise.…”

Section: Introductionmentioning

confidence: 98%

The stochastic primitive equations with transport noise and turbulent pressure

Agresti¹,

Hieber²,

Hussein³

et al. 2021

Preprint

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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 existence and uniqueness of solutions to this stochastic partial differential equation are proven using stochastic maximal L 2regularity, the theory of critical spaces for stochastic evolution equations, and global a priori bounds. Compared to other results in this direction, we do not need any smallness assumption on the transport noise which acts directly on the velocity field and we also allow rougher noise terms. The adaptation to Stratonovich type noise and, more generally, to variable viscosity and/or conductivity are discussed as well. Contents 1. Introduction 1 2. Preliminaries 6 3. Local and global existence in the strong-weak setting 8 4. L 2 -estimates for the linearized problem 14 5. Proof of the main results in the strong-weak setting 21 6. Local and global existence in the strong-strong setting 39 7. Inhomogeneous viscosity and conductivity 49 8. Transport noise of Stratonovich type 55 Appendix A. Kadlec's formulas 59 References 62

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“…nonlocal) SPDEs. Like here, [82] and [25] establish strong convergence for the fluctuations, while [53] even provides a rate of convergence which is shown to be optimal. An alternative pathwise approach to CLTs for SPDEs is being developed in [54], in the context of Landau-Lifschitz equation.…”

Section: Central Limit Theorems For Spdesmentioning

confidence: 54%

“…Another class of CLTs for parabolic SPDEs with multiplicative noise can be found in [20,58,59]. All of the above works however do not include the case of multiplicative transport noise; in this sense, a much closer paper to our setting is the one by Slavík [82], proving an LDP, MDP and CLT for stochastic 3D viscous primitive equations. At the same time the equation considered in [82] is truly parabolic, while our setting is of hyperbolic nature with conservative noise, which makes it closer to the results obtained in [25] (resp.…”

Section: Central Limit Theorems For Spdesmentioning

confidence: 99%

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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Large and Moderate Deviations Principles and Central Limit Theorem for the Stochastic 3D Primitive Equations with Gradient-Dependent Noise

Cited by 6 publications

References 38 publications

Stochastic Primitive Equations with Horizontal Viscosity and Diffusivity

Stochastic Primitive Equations with Horizontal Viscosity and Diffusivity

The stochastic primitive equations with transport noise and turbulent pressure

LDP and CLT for SPDEs with transport noise

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