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The primitive equations formulated in mean vorticity
1. | Department of Mathematics, Indiana University, Bloomington, IN 47405-5701 |
[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) : 1143-1172. doi: 10.3934/dcdsb.2004.4.1143 |
[2] |
Juan Li, Wenqiang Li. Controlled reflected mean-field backward stochastic differential equations coupled with value function and related PDEs. Mathematical Control and Related Fields, 2015, 5 (3) : 501-516. doi: 10.3934/mcrf.2015.5.501 |
[3] |
Silvia Sastre-Gomez. Equivalent formulations for steady periodic water waves of fixed mean-depth with discontinuous vorticity. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2669-2680. doi: 10.3934/dcds.2017114 |
[4] |
Chang-Shou Lin. An expository survey on the recent development of mean field equations. Discrete and Continuous Dynamical Systems, 2007, 19 (2) : 387-410. doi: 10.3934/dcds.2007.19.387 |
[5] |
Pierre-Emmanuel Jabin. A review of the mean field limits for Vlasov equations. Kinetic and Related Models, 2014, 7 (4) : 661-711. doi: 10.3934/krm.2014.7.661 |
[6] |
Michael Herty, Lorenzo Pareschi, Sonja Steffensen. Mean--field control and Riccati equations. Networks and Heterogeneous Media, 2015, 10 (3) : 699-715. doi: 10.3934/nhm.2015.10.699 |
[7] |
Y. Goto, K. Ishii, T. Ogawa. Method of the distance function to the Bence-Merriman-Osher algorithm for motion by mean curvature. Communications on Pure and Applied Analysis, 2005, 4 (2) : 311-339. doi: 10.3934/cpaa.2005.4.311 |
[8] |
Yufeng Shi, Tianxiao Wang, Jiongmin Yong. Mean-field backward stochastic Volterra integral equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (7) : 1929-1967. doi: 10.3934/dcdsb.2013.18.1929 |
[9] |
Bixiang Wang. Mean-square random invariant manifolds for stochastic differential equations. Discrete and Continuous Dynamical Systems, 2021, 41 (3) : 1449-1468. 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) : 2403-2418. doi: 10.3934/cpaa.2020105 |
[11] |
Franco Flandoli, Marta Leocata, Cristiano Ricci. The Vlasov-Navier-Stokes equations as a mean field limit. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 3741-3753. 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) : 5709-5736. 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) : 1719-1742. doi: 10.3934/cpaa.2016010 |
[14] |
Hailong Zhu, Jifeng Chu, Weinian Zhang. Mean-square almost automorphic solutions for stochastic differential equations with hyperbolicity. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 1935-1953. 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) : 931-973. doi: 10.3934/dcds.2010.28.931 |
[16] |
Chiun-Chuan Chen, Chang-Shou Lin. Mean field equations of Liouville type with singular data: Sharper estimates. Discrete and Continuous Dynamical Systems, 2010, 28 (3) : 1237-1272. 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) : 3879-3900. 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) : 4567-4592. doi: 10.3934/dcds.2021049 |
[19] |
Michael Herty, Torsten Trimborn, Giuseppe Visconti. Mean-field and kinetic descriptions of neural differential equations. Foundations of Data Science, 2022, 4 (2) : 271-298. doi: 10.3934/fods.2022007 |
[20] |
Yinggu Chen, Said HamadÈne, Tingshu Mu. Mean-field doubly reflected backward stochastic differential equations. Numerical Algebra, Control and Optimization, 2022 doi: 10.3934/naco.2022012 |
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