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The primitive equations formulated in mean vorticity
1.  Department of Mathematics, Indiana University, Bloomington, IN 474055701 
[1] 
Cheng Wang. Convergence analysis of the numerical method for the primitive equations formulated in mean vorticity on a Cartesian grid. Discrete and Continuous Dynamical Systems  B, 2004, 4 (4) : 11431172. doi: 10.3934/dcdsb.2004.4.1143 
[2] 
Juan Li, Wenqiang Li. Controlled reflected meanfield backward stochastic differential equations coupled with value function and related PDEs. Mathematical Control and Related Fields, 2015, 5 (3) : 501516. doi: 10.3934/mcrf.2015.5.501 
[3] 
Silvia SastreGomez. Equivalent formulations for steady periodic water waves of fixed meandepth with discontinuous vorticity. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 26692680. doi: 10.3934/dcds.2017114 
[4] 
ChangShou Lin. An expository survey on the recent development of mean field equations. Discrete and Continuous Dynamical Systems, 2007, 19 (2) : 387410. doi: 10.3934/dcds.2007.19.387 
[5] 
PierreEmmanuel Jabin. A review of the mean field limits for Vlasov equations. Kinetic and Related Models, 2014, 7 (4) : 661711. doi: 10.3934/krm.2014.7.661 
[6] 
Michael Herty, Lorenzo Pareschi, Sonja Steffensen. Meanfield control and Riccati equations. Networks and Heterogeneous Media, 2015, 10 (3) : 699715. doi: 10.3934/nhm.2015.10.699 
[7] 
Y. Goto, K. Ishii, T. Ogawa. Method of the distance function to the BenceMerrimanOsher algorithm for motion by mean curvature. Communications on Pure and Applied Analysis, 2005, 4 (2) : 311339. doi: 10.3934/cpaa.2005.4.311 
[8] 
Yufeng Shi, Tianxiao Wang, Jiongmin Yong. Meanfield backward stochastic Volterra integral equations. Discrete and Continuous Dynamical Systems  B, 2013, 18 (7) : 19291967. doi: 10.3934/dcdsb.2013.18.1929 
[9] 
Bixiang Wang. Meansquare random invariant manifolds for stochastic differential equations. Discrete and Continuous Dynamical Systems, 2021, 41 (3) : 14491468. doi: 10.3934/dcds.2020324 
[10] 
Wei Wang, Kai Liu, Xiulian Wang. Sensitivity to small delays of mean square stability for stochastic neutral evolution equations. Communications on Pure and Applied Analysis, 2020, 19 (4) : 24032418. doi: 10.3934/cpaa.2020105 
[11] 
Franco Flandoli, Marta Leocata, Cristiano Ricci. The VlasovNavierStokes equations as a mean field limit. Discrete and Continuous Dynamical Systems  B, 2019, 24 (8) : 37413753. doi: 10.3934/dcdsb.2018313 
[12] 
Zhen Li, Jicheng Liu. Synchronization for stochastic differential equations with nonlinear multiplicative noise in the mean square sense. Discrete and Continuous Dynamical Systems  B, 2019, 24 (10) : 57095736. doi: 10.3934/dcdsb.2019103 
[13] 
Jinju Xu. A new proof of gradient estimates for mean curvature equations with oblique boundary conditions. Communications on Pure and Applied Analysis, 2016, 15 (5) : 17191742. doi: 10.3934/cpaa.2016010 
[14] 
Hailong Zhu, Jifeng Chu, Weinian Zhang. Meansquare almost automorphic solutions for stochastic differential equations with hyperbolicity. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 19351953. doi: 10.3934/dcds.2018078 
[15] 
Gabriella Tarantello. Analytical, geometrical and topological aspects of a class of mean field equations on surfaces. Discrete and Continuous Dynamical Systems, 2010, 28 (3) : 931973. doi: 10.3934/dcds.2010.28.931 
[16] 
ChiunChuan Chen, ChangShou Lin. Mean field equations of Liouville type with singular data: Sharper estimates. Discrete and Continuous Dynamical Systems, 2010, 28 (3) : 12371272. doi: 10.3934/dcds.2010.28.1237 
[17] 
Yves Achdou, Mathieu Laurière. On the system of partial differential equations arising in mean field type control. Discrete and Continuous Dynamical Systems, 2015, 35 (9) : 38793900. doi: 10.3934/dcds.2015.35.3879 
[18] 
Hongjie Dong, Xinghong Pan. On conormal derivative problem for parabolic equations with Dini mean oscillation coefficients. Discrete and Continuous Dynamical Systems, 2021, 41 (10) : 45674592. doi: 10.3934/dcds.2021049 
[19] 
Michael Herty, Torsten Trimborn, Giuseppe Visconti. Meanfield and kinetic descriptions of neural differential equations. Foundations of Data Science, 2022, 4 (2) : 271298. doi: 10.3934/fods.2022007 
[20] 
Yinggu Chen, Said HamadÈne, Tingshu Mu. Meanfield doubly reflected backward stochastic differential equations. Numerical Algebra, Control and Optimization, 2022 doi: 10.3934/naco.2022012 
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