Pullback Measure Attractors, Zero-Noise Limits, and Moderate Deviations for 2D Stochastic Primitive Equations with Multiplicative Lévy Noise
Abstract
We study the long-term distributional dynamics and small-noise asymptotics of two-dimensional nonautonomous stochastic primitive equations driven by Gaussian and multiplicative Lévy noise, together with moderate deviations for the purely jump model. For sufficiently small noise, uniform moment bounds and an exponentially weighted terminal estimate yield a pullback absorbing family and tightness, while a lower semicontinuous vertical-moment functional preserves admissibility under weak limits. We prove the existence and uniqueness of a pullback measure attractor in the weak topology of probability measures and establish its upper semicontinuity as both noise components vanish. For the jump-driven equation, we establish a moderate deviation principle in 𝒟([0,T];H)∩ L2(0,T;V) with speed a2(ε)/ε. The proof combines continuity of the skeleton map with controlled stochastic convergence based on entropy bounds, truncation, martingale estimates, and direct vertical estimates, avoiding Lipschitz continuity of the vertical derivative of the jump coefficient.
Related
- Well-posedness and large deviations for 3D primitive equations with jumps
- Large Deviations of Invariant Measures of Fractional Reaction-Diffusion Equations Driven by Multiplicative Noise on R^n
- 𝒟-Pullback Measure Attractors of McKean-Vlasov Stochastic Lattice Wave Equations
- Weak Averaging Principle and Weak Pullback Attractors for Mckean--Vlasov Stochastic Navier--Stokes Equations
- Global well-posedness of the primitive equations with stochastic wind-driven boundary conditions
BibTeX
@misc{zhang2026pullback,
title = {{Pullback Measure Attractors, Zero-Noise Limits, and Moderate Deviations for 2D Stochastic Primitive Equations with Multiplicative Lévy Noise}},
author = {Jiangwei Zhang and Boling Guo and Juntao Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03750},
eprint = {2609.03750},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03750},
}
RIS
TY - UNPB
TI - Pullback Measure Attractors, Zero-Noise Limits, and Moderate Deviations for 2D Stochastic Primitive Equations with Multiplicative Lévy Noise
AU - Jiangwei Zhang
AU - Boling Guo
AU - Juntao Wu
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03750
UR - https://arxiv.org/abs/2609.03750
AB - We study the long-term distributional dynamics and small-noise asymptotics of two-dimensional nonautonomous stochastic primitive equations driven by Gaussian and multiplicative Lévy noise, together with moderate deviations for the purely jump model. For sufficiently small noise, uniform moment bounds and an exponentially weighted terminal estimate yield a pullback absorbing family and tightness, while a lower semicontinuous vertical-moment functional preserves admissibility under weak limits. We prove the existence and uniqueness of a pullback measure attractor in the weak topology of probability measures and establish its upper semicontinuity as both noise components vanish. For the jump-driven equation, we establish a moderate deviation principle in 𝒟([0,T];H)∩ L^2(0,T;V) with speed a^2(ε)/ε. The proof combines continuity of the skeleton map with controlled stochastic convergence based on entropy bounds, truncation, martingale estimates, and direct vertical estimates, avoiding Lipschitz continuity of the vertical derivative of the jump coefficient.
ER -