Well-posedness and large deviations for 3D primitive equations with jumps
Abstract
We establish the global pathwise well-posedness and a Freidlin--Wentzell large deviation principle for the three-dimensional viscous primitive equations driven by multiplicative Lévy noise represented by a compensated Poisson random measure. Under local Lipschitz and moment growth assumptions on the noise coefficient, we construct local martingale solutions and obtain a unique maximal pathwise solution with càdlàg trajectories in the H1 energy space. Additional sixth-moment growth in H1 and L6 growth bounds on the baroclinic component of the noise yield global pathwise well-posedness. The proof combines the jump Itô formula with baroclinic and anisotropic energy estimates to rule out finite-time blow-up. Under further exponential integrability and structural assumptions on the noise coefficient, we establish a Freidlin--Wentzell large deviation principle in a strong path topology by the weak convergence approach.
Related
- Global well-posedness of the primitive equations with stochastic wind-driven boundary conditions
- Pullback Measure Attractors, Zero-Noise Limits, and Moderate Deviations for 2D Stochastic Primitive Equations with Multiplicative Lévy Noise
- Global well-posedness for the 2D primitive equations with subcritical horizontal dissipation
- Global Well-Posedness and Persistence of H2 Regularity for the Three-Dimensional Primitive Equations with Horizontal and Topography-Adapted Thermal Diffusion
- Local Hadamard well-posedness of the 2D primitive equations without thermal diffusion under strict stratification
BibTeX
@misc{shen2026wellposedness,
title = {{Well-posedness and large deviations for 3D primitive equations with jumps}},
author = {Zhuoyang Shen and Xinhua Li and Chunyou Sun},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07274},
eprint = {2611.07274},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07274},
}
RIS
TY - UNPB
TI - Well-posedness and large deviations for 3D primitive equations with jumps
AU - Zhuoyang Shen
AU - Xinhua Li
AU - Chunyou Sun
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07274
UR - https://arxiv.org/abs/2611.07274
AB - We establish the global pathwise well-posedness and a Freidlin--Wentzell large deviation principle for the three-dimensional viscous primitive equations driven by multiplicative Lévy noise represented by a compensated Poisson random measure. Under local Lipschitz and moment growth assumptions on the noise coefficient, we construct local martingale solutions and obtain a unique maximal pathwise solution with càdlàg trajectories in the H^1 energy space. Additional sixth-moment growth in H^1 and L^6 growth bounds on the baroclinic component of the noise yield global pathwise well-posedness. The proof combines the jump Itô formula with baroclinic and anisotropic energy estimates to rule out finite-time blow-up. Under further exponential integrability and structural assumptions on the noise coefficient, we establish a Freidlin--Wentzell large deviation principle in a strong path topology by the weak convergence approach.
ER -