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Convergence analysis of the numerical method for the primitive equations formulated in mean vorticity on a Cartesian grid
1.  Department of Mathematics, University of Tennessee, Knoxville, TN 37996, United States 
[1] 
Cheng Wang. The primitive equations formulated in mean vorticity. Conference Publications, 2003, 2003 (Special) : 880887. doi: 10.3934/proc.2003.2003.880 
[2] 
Juan Li, Wenqiang Li. Controlled reflected meanfield backward stochastic differential equations coupled with value function and related PDEs. Mathematical Control & Related Fields, 2015, 5 (3) : 501516. doi: 10.3934/mcrf.2015.5.501 
[3] 
Josu Doncel, Nicolas Gast, Bruno Gaujal. Discrete mean field games: Existence of equilibria and convergence. Journal of Dynamics & Games, 2019, 6 (3) : 221239. doi: 10.3934/jdg.2019016 
[4] 
Chuchu Chen, Jialin Hong. Meansquare convergence of numerical approximations for a class of backward stochastic differential equations. Discrete & Continuous Dynamical Systems  B, 2013, 18 (8) : 20512067. doi: 10.3934/dcdsb.2013.18.2051 
[5] 
Bin Pei, Yong Xu, Yuzhen Bai. Convergence of pth mean in an averaging principle for stochastic partial differential equations driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems  B, 2017, 22 (11) : 00. doi: 10.3934/dcdsb.2019213 
[6] 
Evelyn Buckwar, Girolama Notarangelo. A note on the analysis of asymptotic meansquare stability properties for systems of linear stochastic delay differential equations. Discrete & Continuous Dynamical Systems  B, 2013, 18 (6) : 15211531. doi: 10.3934/dcdsb.2013.18.1521 
[7] 
Silvia SastreGomez. Equivalent formulations for steady periodic water waves of fixed meandepth with discontinuous vorticity. Discrete & Continuous Dynamical Systems  A, 2017, 37 (5) : 26692680. doi: 10.3934/dcds.2017114 
[8] 
ChangShou Lin. An expository survey on the recent development of mean field equations. Discrete & Continuous Dynamical Systems  A, 2007, 19 (2) : 387410. doi: 10.3934/dcds.2007.19.387 
[9] 
PierreEmmanuel Jabin. A review of the mean field limits for Vlasov equations. Kinetic & Related Models, 2014, 7 (4) : 661711. doi: 10.3934/krm.2014.7.661 
[10] 
Michael Herty, Lorenzo Pareschi, Sonja Steffensen. Meanfield control and Riccati equations. Networks & Heterogeneous Media, 2015, 10 (3) : 699715. doi: 10.3934/nhm.2015.10.699 
[11] 
Hayato Chiba, Georgi S. Medvedev. The mean field analysis of the Kuramoto model on graphs Ⅰ. The mean field equation and transition point formulas. Discrete & Continuous Dynamical Systems  A, 2019, 39 (1) : 131155. doi: 10.3934/dcds.2019006 
[12] 
Makram Hamouda, ChangYeol Jung, Roger Temam. Asymptotic analysis for the 3D primitive equations in a channel. Discrete & Continuous Dynamical Systems  S, 2013, 6 (2) : 401422. doi: 10.3934/dcdss.2013.6.401 
[13] 
Illés Horváth, Kristóf Attila Horváth, Péter Kovács, Miklós Telek. Meanfield analysis of a scaling MAC radio protocol. Journal of Industrial & Management Optimization, 2017, 13 (5) : 00. doi: 10.3934/jimo.2019111 
[14] 
Y. Goto, K. Ishii, T. Ogawa. Method of the distance function to the BenceMerrimanOsher algorithm for motion by mean curvature. Communications on Pure & Applied Analysis, 2005, 4 (2) : 311339. doi: 10.3934/cpaa.2005.4.311 
[15] 
Oleksandr Misiats, Nung Kwan Yip. Convergence of spacetime discrete threshold dynamics to anisotropic motion by mean curvature. Discrete & Continuous Dynamical Systems  A, 2016, 36 (11) : 63796411. doi: 10.3934/dcds.2016076 
[16] 
Yufeng Shi, Tianxiao Wang, Jiongmin Yong. Meanfield backward stochastic Volterra integral equations. Discrete & Continuous Dynamical Systems  B, 2013, 18 (7) : 19291967. doi: 10.3934/dcdsb.2013.18.1929 
[17] 
Jinju Xu. A new proof of gradient estimates for mean curvature equations with oblique boundary conditions. Communications on Pure & Applied Analysis, 2016, 15 (5) : 17191742. doi: 10.3934/cpaa.2016010 
[18] 
Hailong Zhu, Jifeng Chu, Weinian Zhang. Meansquare almost automorphic solutions for stochastic differential equations with hyperbolicity. Discrete & Continuous Dynamical Systems  A, 2018, 38 (4) : 19351953. doi: 10.3934/dcds.2018078 
[19] 
Gabriella Tarantello. Analytical, geometrical and topological aspects of a class of mean field equations on surfaces. Discrete & Continuous Dynamical Systems  A, 2010, 28 (3) : 931973. doi: 10.3934/dcds.2010.28.931 
[20] 
ChiunChuan Chen, ChangShou Lin. Mean field equations of Liouville type with singular data: Sharper estimates. Discrete & Continuous Dynamical Systems  A, 2010, 28 (3) : 12371272. doi: 10.3934/dcds.2010.28.1237 
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