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Energetic variational approach in complex fluids: Maximum dissipation principle
1.  Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, MN 55455, United States 
2.  Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon 305701, South Korea 
3.  Department of Mathematics, The Pennsylvania State University, University Park, PA 16802 
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Bin Han, Changhua Wei. Global wellposedness for inhomogeneous NavierStokes equations with logarithmical hyperdissipation. Discrete & Continuous Dynamical Systems, 2016, 36 (12) : 69216941. doi: 10.3934/dcds.2016101 
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BoQing Dong, Juan Song. Global regularity and asymptotic behavior of modified NavierStokes equations with fractional dissipation. Discrete & Continuous Dynamical Systems, 2012, 32 (1) : 5779. doi: 10.3934/dcds.2012.32.57 
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Shuguang Shao, Shu Wang, WenQing Xu. Global regularity for a model of NavierStokes equations with logarithmic subdissipation. Kinetic & Related Models, 2018, 11 (1) : 179190. doi: 10.3934/krm.2018009 
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Hongjie Dong, Dong Li. On a generalized maximum principle for a transportdiffusion model with $\log$modulated fractional dissipation. Discrete & Continuous Dynamical Systems, 2014, 34 (9) : 34373454. doi: 10.3934/dcds.2014.34.3437 
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Anna Amirdjanova, Jie Xiong. Large deviation principle for a stochastic navierStokes equation in its vorticity form for a twodimensional incompressible flow. Discrete & Continuous Dynamical Systems  B, 2006, 6 (4) : 651666. doi: 10.3934/dcdsb.2006.6.651 
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Huaiqiang Yu, Bin Liu. Pontryagin's principle for local solutions of optimal control governed by the 2D NavierStokes equations with mixed controlstate constraints. Mathematical Control & Related Fields, 2012, 2 (1) : 6180. doi: 10.3934/mcrf.2012.2.61 
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Yanlin Liu, Ping Zhang. Remark on 3D NavierStokes system with strong dissipation in one direction. Communications on Pure & Applied Analysis, , () : . doi: 10.3934/cpaa.2020244 
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Nassif Ghoussoub. A variational principle for nonlinear transport equations. Communications on Pure & Applied Analysis, 2005, 4 (4) : 735742. doi: 10.3934/cpaa.2005.4.735 
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Jie Jiang, Yinghua Li, Chun Liu. Twophase incompressible flows with variable density: An energetic variational approach. Discrete & Continuous Dynamical Systems, 2017, 37 (6) : 32433284. doi: 10.3934/dcds.2017138 
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C. Foias, M. S Jolly, I. Kukavica, E. S. Titi. The Lorenz equation as a metaphor for the NavierStokes equations. Discrete & Continuous Dynamical Systems, 2001, 7 (2) : 403429. doi: 10.3934/dcds.2001.7.403 
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H. O. Fattorini. The maximum principle in infinite dimension. Discrete & Continuous Dynamical Systems, 2000, 6 (3) : 557574. doi: 10.3934/dcds.2000.6.557 
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Peter Anthony, Sergey Zelik. Infiniteenergy solutions for the NavierStokes equations in a strip revisited. Communications on Pure & Applied Analysis, 2014, 13 (4) : 13611393. doi: 10.3934/cpaa.2014.13.1361 
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José Luiz Boldrini, Luís H. de Miranda, Gabriela Planas. On singular NavierStokes equations and irreversible phase transitions. Communications on Pure & Applied Analysis, 2012, 11 (5) : 20552078. doi: 10.3934/cpaa.2012.11.2055 
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Ariane Piovezan Entringer, José Luiz Boldrini. A phase field $\alpha$NavierStokes vesiclefluid interaction model: Existence and uniqueness of solutions. Discrete & Continuous Dynamical Systems  B, 2015, 20 (2) : 397422. doi: 10.3934/dcdsb.2015.20.397 
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Qiang Du, Manlin Li, Chun Liu. Analysis of a phase field NavierStokes vesiclefluid interaction model. Discrete & Continuous Dynamical Systems  B, 2007, 8 (3) : 539556. doi: 10.3934/dcdsb.2007.8.539 
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Francesca Da Lio. Remarks on the strong maximum principle for viscosity solutions to fully nonlinear parabolic equations. Communications on Pure & Applied Analysis, 2004, 3 (3) : 395415. doi: 10.3934/cpaa.2004.3.395 
[19] 
Yu Tian, John R. Graef, Lingju Kong, Min Wang. Existence of solutions to a multipoint boundary value problem for a second order differential system via the dual least action principle. Conference Publications, 2013, 2013 (special) : 759769. doi: 10.3934/proc.2013.2013.759 
[20] 
Ricardo Almeida, Agnieszka B. Malinowska. Fractional variational principle of Herglotz. Discrete & Continuous Dynamical Systems  B, 2014, 19 (8) : 23672381. doi: 10.3934/dcdsb.2014.19.2367 
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