Well-posedness of stochastic 2D hydrodynamics type systems with multiplicative Lévy noises

@article{Peng2022WellposednessOS,
  title={Well-posedness of stochastic 2D hydrodynamics type systems with multiplicative L{\'e}vy noises},
  author={Xuhui Peng and Juan Yang and Jianliang Zhai},
  journal={Electronic Journal of Probability},
  year={2022}
}
We establish the existence and uniqueness of solutions to an abstract nonlinear equation driven by a multiplicative noise of Levy type, which covers many hydrodynamical models including 2D Navier-Stokes equations, 2D MHD equations, the 2D Magnetic Bernard problem, and several Shell models of turbulence. In the existing literature on this topic, besides the classical Lipschitz and one sided linear growth conditions, other assumptions, which might be untypical, are also required on the… 

References

SHOWING 1-10 OF 46 REFERENCES

Well-posedness and large deviations for 2D stochastic Navier–Stokes equations with jumps

Under the classical local Lipschitz and one sided linear growth assumptions on the coefficients of the stochastic perturbations, we first prove the existence and the uniqueness of a strong (in both

Strong solutions to stochastic hydrodynamical systems with multiplicative noise of jump type

In this paper we prove the existence and uniqueness of maximal strong (in PDE sense) solution to several stochastic hydrodynamical systems on unbounded and bounded domains of $${\mathbb{R}^n}$$Rn, n

Stochastic 2D Hydrodynamical Type Systems: Well Posedness and Large Deviations

We deal with a class of abstract nonlinear stochastic models, which covers many 2D hydrodynamical models including 2D Navier-Stokes equations, 2D MHD models and the 2D magnetic Bénard problem and

Martingale solutions for stochastic Navier-Stokes equations driven by Lévy noise

In this paper, we establish the solvability of martingale solutions for the stochastic Navier-Stokes equations with Ito-Levy noise in bounded and unbounded domains in $ \mathbb{R} ^d$,$d=2,3.$ The

Stochastic Navier–Stokes Equations Driven by Lévy Noise in Unbounded 3D Domains

Martingale solutions of the stochastic Navier–Stokes equations in 2D and 3D possibly unbounded domains, driven by the Lévy noise consisting of the compensated time homogeneous Poisson random measure

Stochastic tamed 3D Navier–Stokes equations: existence, uniqueness and ergodicity

In this paper, we prove the existence of a unique strong solution to a stochastic tamed 3D Navier–Stokes equation in the whole space as well as in the periodic boundary case. Then, we also study the

2D stochastic Navier–Stokes equations driven by jump noise

Global L2-solutions of stochastic Navier–Stokes equations

This paper concerns the Cauchy problem in R d for the stochastic Navier-Stokes equation ∂ 1 u = Δu - (u, ⊇)u - ⊇ p + f(u) + [(σ, ⊇)u - ⊇p + g(u)] o W. u(0) = u 0 , div u = 0, driven by white noise W.

Exponential Convergence for the Stochastically Forced Navier-Stokes Equations and Other Partially Dissipative Dynamics

Abstract: We prove that the two dimensional Navier-Stokes equations possess an exponentially attracting invariant measure. This result is in fact the consequence of a more general ``Harris-like''