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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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Stefan Doboszczak, Manil T. Mohan, Sivaguru S. Sritharan. Pontryagin maximum principle for the optimal control of linearized compressible navierstokes equations with state constraints. Evolution Equations and Control Theory, 2022, 11 (2) : 347371. doi: 10.3934/eect.2020110 
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Bin Han, Changhua Wei. Global wellposedness for inhomogeneous NavierStokes equations with logarithmical hyperdissipation. Discrete and 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 and 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 and 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 and 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 and 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 and 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 and Applied Analysis, 2021, 20 (7&8) : 27652787. doi: 10.3934/cpaa.2020244 
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Yat Tin Chow, Ali Pakzad. On the zeroth law of turbulence for the stochastically forced NavierStokes equations. Discrete and Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021270 
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Nassif Ghoussoub. A variational principle for nonlinear transport equations. Communications on Pure and 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 and 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 and 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 and 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 and 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 and Applied Analysis, 2012, 11 (5) : 20552078. doi: 10.3934/cpaa.2012.11.2055 
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M. Hassan FarshbafShaker, Harald Garcke. Thermodynamically consistent higher order phase field NavierStokes models with applications to biomembranes. Discrete and Continuous Dynamical Systems  S, 2011, 4 (2) : 371389. doi: 10.3934/dcdss.2011.4.371 
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Ariane Piovezan Entringer, José Luiz Boldrini. A phase field $\alpha$NavierStokes vesiclefluid interaction model: Existence and uniqueness of solutions. Discrete and 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 and Continuous Dynamical Systems  B, 2007, 8 (3) : 539556. doi: 10.3934/dcdsb.2007.8.539 
[19] 
Francesca Da Lio. Remarks on the strong maximum principle for viscosity solutions to fully nonlinear parabolic equations. Communications on Pure and Applied Analysis, 2004, 3 (3) : 395415. doi: 10.3934/cpaa.2004.3.395 
[20] 
XiaoLi Ding, Iván Area, Juan J. Nieto. Controlled singular evolution equations and Pontryagin type maximum principle with applications. Evolution Equations and Control Theory, 2021 doi: 10.3934/eect.2021059 
2020 Impact Factor: 1.392
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