Asymptotic log-Harnack inequality and applications for stochastic 2D hydrodynamical-type systems with degenerate noise

Hong, Wei; Li, Shihu; Liu, Wei

doi:10.1007/s00028-020-00587-w

Cited by 11 publications

(8 citation statements)

References 38 publications

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“…Applying Theorem 2.1, [4], similar results obtained in Corollary 3.1, [20], we have the following corollary.…”

Section: Asymptotic Log-harnack Inequalitysupporting

confidence: 73%

“…and we denote H l := P N 0 H and H h := (I − P N 0 )H. For any u ∈ H, we define u l := P N 0 u and u h := (I − P N 0 )u. The following lemma is easy to prove and one can get a proof from Lemma 3.2, [20].…”

Section: Definition 21 ([3]mentioning

confidence: 99%

“…In this section, we establish the asymptotic log-Harnack inequality for the trasition semigroup associated with the stochastic convective Brinkman-Forchheimer equations (2.17) and discuss about its consequences. Asymptotic log-Harnack inequality for stochastic 2D hydrodynamical-type systems with degenerate noise is obtained in [20] and we mainly follow this work to obtain our main results.…”

Section: Asymptotic Log-harnack Inequalitymentioning

confidence: 99%

“…By using the asymptotic coupling method, the asymptotic log-Harnack inequality for the transition semigroup associated to the 3D Leray-α model with fractional dissipation driven by highly degenerate noise is established in [26]. The asymptotic log-Harnack inequality and some of its consequent properties for a class of stochastic 2D hydrodynamical-type systems driven by degenerate noise are established in [20]. In [21], the authors established asymptotic log-Harnack inequality and discussed its applications for semilinear SPDEs with degenerate multiplicative noise by the coupling method.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic log-Harnack inequality for the stochastic convective Brinkman-Forchheimer equations with degenerate noise

Mohan

2020

Preprint

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In this work, we consider the two and three dimensional stochastic convective Brinkman-Forchheimer (SCBF) equations and examine some asymptotic behaviors of its strong solution. We establish the asymptotic log-Harnack inequality for the transition semigroup associated with the SCBF equations driven by additive as well as multiplicative degenerate noise via the asymptotic coupling method. As applications of the asymptotic log-Harnack inequality, we derive the gradient estimate, asymptotic irreducibility, asymptotic strong Feller property, asymptotic heat kernel estimate and ergodicity. Whenever the absorption exponent r ∈ (3, ∞), the asymptotic log-Harnack inequality is obtained without any restriction on the Brinkman coefficient (effective viscosity) µ > 0, the Darcy coefficient α > 0 and the Forchheimer coefficient β > 0.

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“…Applying Theorem 2.1, [4], similar results obtained in Corollary 3.1, [20], we have the following corollary.…”

Section: Asymptotic Log-harnack Inequalitysupporting

confidence: 73%

Section: Definition 21 ([3]mentioning

confidence: 99%

Section: Asymptotic Log-harnack Inequalitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Asymptotic log-Harnack inequality for the stochastic convective Brinkman-Forchheimer equations with degenerate noise

Mohan

2020

Preprint

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“…(ii) Based on the work of [6], the main result obtained in this subsection is applicable to many concrete hydrodynamical type systems, for instance, the stochastic 2D Navier-Stokes equation, stochastic 2D magneto-hydrodynamic equations, stochastic 2D Boussinesq equations, stochastic 2D magnetic Bénard problem, stochastic 3D Leray-α model and also shell models of turbulence. We also refer the reader to [9,15,16] and references within for the mathematical treatment and further studies of these models.…”

Section: Stochastic 2d Hydrodynamical Type Systemsmentioning

confidence: 99%

Freidlin-Wentzell Type Large Deviation Principle for Multi-Scale Locally Monotone SPDEs

Hong¹,

Li²,

Liu³

2021

Preprint

Self Cite

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This work is concerned with the Freidlin-Wentzell type large deviation principle for a family of multi-scale quasi-linear and semi-linear stochastic partial differential equations (SPDEs) with small multiplicative noise under the generalized variational setting, which extend several existing works to the multiscale process. Employing the weak convergence method developed by Dupuis and Ellis [7] and Khasminskii's time discretization approach [18], the Laplace principle for SPDEs will be derived, which is equivalent to the large deviation principle. In particular, in this paper, we do not assume any compactness of the embedding on the Gelfand triple we considered in order to deal with the case of bounded and unbounded domains in some concrete models. Our main results are applicable to a wide family of SPDEs such as stochastic porous media equations, stochastic fast-diffusion equations, stochastic 2D hydrodynamical type models, stochastic p-Laplace equations, stochastic power law fluid equations and stochastic Ladyzhenskaya models.

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Asymptotic Log-Harnack Inequality and Ergodicity for 3D Leray-α Model with Degenerate Type Noise

Hong

Liu

2020

Potential Anal

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Asymptotic log-Harnack inequality and applications for stochastic 2D hydrodynamical-type systems with degenerate noise

Cited by 11 publications

References 38 publications

Asymptotic log-Harnack inequality for the stochastic convective Brinkman-Forchheimer equations with degenerate noise

Asymptotic log-Harnack inequality for the stochastic convective Brinkman-Forchheimer equations with degenerate noise

Freidlin-Wentzell Type Large Deviation Principle for Multi-Scale Locally Monotone SPDEs

Asymptotic Log-Harnack Inequality and Ergodicity for 3D Leray-α Model with Degenerate Type Noise

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