The stochastic 2D primitive equations with anisotropic viscosity are studied in this paper. The existence of the martingale solutions and pathwise uniqueness of the solutions are obtained. The proof is based on anisotropic estimates, the compactness method, tightness criteria and the Jakubowski version of the Skorokhod theorem for nonmetric spaces.
Keywords: Stochastic primitive equations, anisotropic viscosity, Martingale solutions
@article{PS_2022__26_1_243_0,
author = {Sun, Chengfeng and Gao, Hongjun and Liu, Hui and Zhang, Jie},
title = {Martingale {Solutions} of the {Stochastic} {2D} {Primitive} {Equations} with {Anisotropic} {Viscosity}},
journal = {ESAIM: Probability and Statistics},
pages = {243--264},
year = {2022},
publisher = {EDP-Sciences},
volume = {26},
doi = {10.1051/ps/2022006},
mrnumber = {4424999},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2022006/}
}
TY - JOUR AU - Sun, Chengfeng AU - Gao, Hongjun AU - Liu, Hui AU - Zhang, Jie TI - Martingale Solutions of the Stochastic 2D Primitive Equations with Anisotropic Viscosity JO - ESAIM: Probability and Statistics PY - 2022 SP - 243 EP - 264 VL - 26 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ps/2022006/ DO - 10.1051/ps/2022006 LA - en ID - PS_2022__26_1_243_0 ER -
%0 Journal Article %A Sun, Chengfeng %A Gao, Hongjun %A Liu, Hui %A Zhang, Jie %T Martingale Solutions of the Stochastic 2D Primitive Equations with Anisotropic Viscosity %J ESAIM: Probability and Statistics %D 2022 %P 243-264 %V 26 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ps/2022006/ %R 10.1051/ps/2022006 %G en %F PS_2022__26_1_243_0
Sun, Chengfeng; Gao, Hongjun; Liu, Hui; Zhang, Jie. Martingale Solutions of the Stochastic 2D Primitive Equations with Anisotropic Viscosity. ESAIM: Probability and Statistics, Tome 26 (2022), pp. 243-264. doi: 10.1051/ps/2022006
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Supported partially by a China NSF Grant Nos. 12171084, 11701269, 11901342, China Postdoctoral Science Foundation No. 2019M652153, the fundamental Research Funds for the Central Universities No. 2242022R10013 and the Natural Science Foundation of Shandong under Grant No. ZR2018QA002.
