Well-posedness and invariant measures for a class of stochastic 3D Navier-Stokes equations with damping driven by jump noise

Gao, Hongjun; Liu, Hui

doi:10.1016/j.jde.2019.06.015

Cited by 24 publications

(10 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Small time large deviations principles for the stochastic 3D tamed Navier-Stokes equations in bounded domains is established in the work [43]. Large deviation principle for 3D tamed Navier-Stokes equations driven by multiplicative Lévy noise in periodic domains is established in [22]. The authors in the work [29] obtained a small time large deviation principle for the stochastic 3D Navier-Stokes equation with damping in bounded domains.…”

Section: Introductionmentioning

confidence: 99%

Moderate deviation principle for the 2D stochastic convective Brinkman–Forchheimer equations

Mohan

2020

Stochastics

View full text Add to dashboard Cite

This work addresses some asymptotic behavior of solutions to the stochastic convective Brinkman-Forchheimer (SCBF) equations perturbed by multiplicative Gaussian noise in bounded domains. Using a weak convergence approach of Budhiraja and Dupuis, we establish the Laplace principle for the strong solution to the SCBF equations in a suitable Polish space. Then, the Wentzell-Freidlin large deviation principle is derived using the well known results of Varadhan and Bryc. The large deviations for short time are also considered in this work. Furthermore, we study the exponential estimates on certain exit times associated with the solution trajectory of the SCBF equations. Using contraction principle, we study these exponential estimates of exit times from the frame of reference of Freidlin-Wentzell type large deviations principle. This work also improves several LDP results available in the literature for the tamed Navier-Stokes equations as well as Navier-Stokes equations with damping in bounded domains.

show abstract

Section: Introductionmentioning

confidence: 99%

Moderate deviation principle for the 2D stochastic convective Brinkman–Forchheimer equations

Mohan

2020

Stochastics

View full text Add to dashboard Cite

show abstract

“…Furthermore, again for the same range, for multiplicative noise, exponential convergence of the weak solutions in L 2 to the stationary solution as well as stabilisation were proved by Liu et al [25]. Finally, the case of jump noise was treated by Liu and Gao [16].…”

Section: Damped Navier-stokes and Mhd Equationsmentioning

confidence: 87%

The stochastic tamed MHD equations: existence, uniqueness and invariant measures

Schenke

2021

Stoch PDE: Anal Comp

View full text Add to dashboard Cite

We study the tamed magnetohydrodynamics equations, introduced recently in a paper by the author, perturbed by multiplicative Wiener noise of transport type on the whole space $${\mathbb {R}}^{3}$$ R 3 and on the torus $${\mathbb {T}}^{3}$$ T 3 . In a first step, existence of a unique strong solution are established by constructing a weak solution, proving that pathwise uniqueness holds and using the Yamada–Watanabe theorem. We then study the associated Markov semigroup and prove that it has the Feller property. Finally, existence of an invariant measure of the equation is shown for the case of the torus.

show abstract

“…To establish this relation, we use the same idea as in [3,8]. For any natural number m ≤ n, let θ be a progressively measurable process belonging to…”

Section: By Riesz Isomorphism We Havementioning

confidence: 99%

Well-posedness for the three dimensional stochastic planetary geostrophic equations of large-scale ocean circulation

You¹

2021

Discrete &Amp; Continuous Dynamical Systems - A

View full text Add to dashboard Cite

The objective of this paper is to study the well-posedness of solutions for the three dimensional planetary geostrophic equations of large-scale ocean circulation with additive noise. Since strong coupling terms and the noise term create some difficulties in the process of showing the existence of weak solutions, we will first show the existence of weak solutions by the monotonicity methods when the initial data satisfies some "regular" condition. For the case of general initial data, we will establish the existence of weak solutions by taking a sequence of "regular" initial data and proving the convergence in probability as well as some weak convergence of the corresponding solution sequences. Finally, we establish the existence of weak D-pullback mean random attractors in the framework developed in [11, 25].

show abstract

Well-posedness and invariant measures for a class of stochastic 3D Navier-Stokes equations with damping driven by jump noise

Cited by 24 publications

References 27 publications

Moderate deviation principle for the 2D stochastic convective Brinkman–Forchheimer equations

Moderate deviation principle for the 2D stochastic convective Brinkman–Forchheimer equations

The stochastic tamed MHD equations: existence, uniqueness and invariant measures

Well-posedness for the three dimensional stochastic planetary geostrophic equations of large-scale ocean circulation

Contact Info

Product

Resources

About