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On energetic variational approaches in modeling the nematic liquid crystal flows
1. | Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, United States |
[1] |
Bum Ja Jin, Kyungkeun Kang. Caccioppoli type inequality for non-Newtonian Stokes system and a local energy inequality of non-Newtonian Navier-Stokes equations without pressure. Discrete and Continuous Dynamical Systems, 2017, 37 (9) : 4815-4834. doi: 10.3934/dcds.2017207 |
[2] |
Lars Diening, Michael Růžička. An existence result for non-Newtonian fluids in non-regular domains. Discrete and Continuous Dynamical Systems - S, 2010, 3 (2) : 255-268. doi: 10.3934/dcdss.2010.3.255 |
[3] |
Jan Sokołowski, Jan Stebel. Shape optimization for non-Newtonian fluids in time-dependent domains. Evolution Equations and Control Theory, 2014, 3 (2) : 331-348. doi: 10.3934/eect.2014.3.331 |
[4] |
Aneta Wróblewska-Kamińska. Unsteady flows of non-Newtonian fluids in generalized Orlicz spaces. Discrete and Continuous Dynamical Systems, 2013, 33 (6) : 2565-2592. doi: 10.3934/dcds.2013.33.2565 |
[5] |
Pitágoras Pinheiro de Carvalho, Juan Límaco, Denilson Menezes, Yuri Thamsten. Local null controllability of a class of non-Newtonian incompressible viscous fluids. Evolution Equations and Control Theory, 2021 doi: 10.3934/eect.2021043 |
[6] |
Yukun Song, Yang Chen, Jun Yan, Shuai Chen. The existence of solutions for a shear thinning compressible non-Newtonian models. Electronic Research Archive, 2020, 28 (1) : 47-66. doi: 10.3934/era.2020004 |
[7] |
Emil Novruzov. On existence and nonexistence of the positive solutions of non-newtonian filtration equation. Communications on Pure and Applied Analysis, 2011, 10 (2) : 719-730. doi: 10.3934/cpaa.2011.10.719 |
[8] |
Wojciech M. Zajączkowski. Long time existence of regular solutions to non-homogeneous Navier-Stokes equations. Discrete and Continuous Dynamical Systems - S, 2013, 6 (5) : 1427-1455. doi: 10.3934/dcdss.2013.6.1427 |
[9] |
Muhammad Mansha Ghalib, Azhar Ali Zafar, Zakia Hammouch, Muhammad Bilal Riaz, Khurram Shabbir. Analytical results on the unsteady rotational flow of fractional-order non-Newtonian fluids with shear stress on the boundary. Discrete and Continuous Dynamical Systems - S, 2020, 13 (3) : 683-693. doi: 10.3934/dcdss.2020037 |
[10] |
Xin Liu, Yongjin Lu, Xin-Guang Yang. Stability and dynamics for a nonlinear one-dimensional full compressible non-Newtonian fluids. Evolution Equations and Control Theory, 2021, 10 (2) : 365-384. doi: 10.3934/eect.2020071 |
[11] |
Zhenhua Guo, Wenchao Dong, Jinjing Liu. Large-time behavior of solution to an inflow problem on the half space for a class of compressible non-Newtonian fluids. Communications on Pure and Applied Analysis, 2019, 18 (4) : 2133-2161. doi: 10.3934/cpaa.2019096 |
[12] |
Daoyuan Fang, Bin Han, Matthias Hieber. Local and global existence results for the Navier-Stokes equations in the rotational framework. Communications on Pure and Applied Analysis, 2015, 14 (2) : 609-622. doi: 10.3934/cpaa.2015.14.609 |
[13] |
Peixin Zhang, Jianwen Zhang, Junning Zhao. On the global existence of classical solutions for compressible Navier-Stokes equations with vacuum. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 1085-1103. doi: 10.3934/dcds.2016.36.1085 |
[14] |
Reinhard Racke, Jürgen Saal. Hyperbolic Navier-Stokes equations II: Global existence of small solutions. Evolution Equations and Control Theory, 2012, 1 (1) : 217-234. doi: 10.3934/eect.2012.1.217 |
[15] |
Zaihong Jiang, Li Li, Wenbo Lu. Existence of axisymmetric and homogeneous solutions of Navier-Stokes equations in cone regions. Discrete and Continuous Dynamical Systems - S, 2021, 14 (12) : 4231-4258. doi: 10.3934/dcdss.2021126 |
[16] |
Hi Jun Choe, Do Wan Kim, Yongsik Kim. Meshfree method for the non-stationary incompressible Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2006, 6 (1) : 17-39. doi: 10.3934/dcdsb.2006.6.17 |
[17] |
Joelma Azevedo, Juan Carlos Pozo, Arlúcio Viana. Global solutions to the non-local Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2022, 27 (5) : 2515-2535. doi: 10.3934/dcdsb.2021146 |
[18] |
Ansgar Jüngel, Josipa-Pina Milišić. Full compressible Navier-Stokes equations for quantum fluids: Derivation and numerical solution. Kinetic and Related Models, 2011, 4 (3) : 785-807. doi: 10.3934/krm.2011.4.785 |
[19] |
Pavel I. Plotnikov, Jan Sokolowski. Compressible Navier-Stokes equations. Conference Publications, 2009, 2009 (Special) : 602-611. doi: 10.3934/proc.2009.2009.602 |
[20] |
Jan W. Cholewa, Tomasz Dlotko. Fractional Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (8) : 2967-2988. doi: 10.3934/dcdsb.2017149 |
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