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An inviscid dyadic model of turbulence: The global attractor
1.  Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 322 Science and Engineering Offices (M/C 249), 851 S. Morgan Street, Chicago, IL 606077045, United States 
2.  Department of Mathematics, University of Southern California, 3620 South Vermont Ave., KAP 108, Los Angeles, CA 90089, United States 
3.  Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200 Austin, Texas 78712 
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Tania Biswas, Sheetal Dharmatti. Control problems and invariant subspaces for sabra shell model of turbulence. Evolution Equations & Control Theory, 2018, 7 (3) : 417445. doi: 10.3934/eect.2018021 
[2] 
I. D. Chueshov, Iryna Ryzhkova. A global attractor for a fluidplate interaction model. Communications on Pure & Applied Analysis, 2013, 12 (4) : 16351656. doi: 10.3934/cpaa.2013.12.1635 
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Rana D. Parshad, Juan B. Gutierrez. On the global attractor of the Trojan Y Chromosome model. Communications on Pure & Applied Analysis, 2011, 10 (1) : 339359. doi: 10.3934/cpaa.2011.10.339 
[4] 
Eleftherios Gkioulekas, Ka Kit Tung. On the double cascades of energy and enstrophy in two dimensional turbulence. Part 1. Theoretical formulation. Discrete & Continuous Dynamical Systems  B, 2005, 5 (1) : 79102. doi: 10.3934/dcdsb.2005.5.79 
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Patrick Fischer, CharlesHenri Bruneau, Hamid Kellay. Multiresolution analysis for 2D turbulence. part 2: A physical interpretation. Discrete & Continuous Dynamical Systems  B, 2007, 7 (4) : 717734. doi: 10.3934/dcdsb.2007.7.717 
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Marcel Lesieur. Twopoint closure based largeeddy simulations in turbulence. Part 2: Inhomogeneous cases. Discrete & Continuous Dynamical Systems  A, 2010, 28 (1) : 227241. doi: 10.3934/dcds.2010.28.227 
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Patrick Fischer. Multiresolution analysis for 2D turbulence. Part 1: Wavelets vs cosine packets, a comparative study. Discrete & Continuous Dynamical Systems  B, 2005, 5 (3) : 659686. doi: 10.3934/dcdsb.2005.5.659 
[8] 
Eleftherios Gkioulekas, Ka Kit Tung. On the double cascades of energy and enstrophy in two dimensional turbulence. Part 2. Approach to the KLB limit and interpretation of experimental evidence. Discrete & Continuous Dynamical Systems  B, 2005, 5 (1) : 103124. doi: 10.3934/dcdsb.2005.5.103 
[9] 
W. Layton, R. Lewandowski. On a wellposed turbulence model. Discrete & Continuous Dynamical Systems  B, 2006, 6 (1) : 111128. doi: 10.3934/dcdsb.2006.6.111 
[10] 
Luca Bisconti, Davide Catania. Global wellposedness of the twodimensional horizontally filtered simplified Bardina turbulence model on a striplike region. Communications on Pure & Applied Analysis, 2017, 16 (5) : 18611881. doi: 10.3934/cpaa.2017090 
[11] 
Inger Daniels, Catherine Lebiedzik. Existence and uniqueness of a structural acoustic model involving a nonlinear shell. Discrete & Continuous Dynamical Systems  S, 2008, 1 (2) : 243252. doi: 10.3934/dcdss.2008.1.243 
[12] 
Sylvia Anicic. Existence theorem for a firstorder Koiter nonlinear shell model. Discrete & Continuous Dynamical Systems  S, 2019, 12 (6) : 15351545. doi: 10.3934/dcdss.2019106 
[13] 
Peter R. Kramer, Joseph A. Biello, Yuri Lvov. Application of weak turbulence theory to FPU model. Conference Publications, 2003, 2003 (Special) : 482491. doi: 10.3934/proc.2003.2003.482 
[14] 
Nobuyuki Kenmochi, Noriaki Yamazaki. Global attractor of the multivalued semigroup associated with a phasefield model of grain boundary motion with constraint. Conference Publications, 2011, 2011 (Special) : 824833. doi: 10.3934/proc.2011.2011.824 
[15] 
T. Tachim Medjo. A nonautonomous 3D Lagrangian averaged NavierStokes$\alpha$ model with oscillating external force and its global attractor. Communications on Pure & Applied Analysis, 2011, 10 (2) : 415433. doi: 10.3934/cpaa.2011.10.415 
[16] 
T. Gallouët, J.C. Latché. Compactness of discrete approximate solutions to parabolic PDEs  Application to a turbulence model. Communications on Pure & Applied Analysis, 2012, 11 (6) : 23712391. doi: 10.3934/cpaa.2012.11.2371 
[17] 
Eduardo Liz, Gergely Röst. On the global attractor of delay differential equations with unimodal feedback. Discrete & Continuous Dynamical Systems  A, 2009, 24 (4) : 12151224. doi: 10.3934/dcds.2009.24.1215 
[18] 
Hiroshi Matano, KenIchi Nakamura. The global attractor of semilinear parabolic equations on $S^1$. Discrete & Continuous Dynamical Systems  A, 1997, 3 (1) : 124. doi: 10.3934/dcds.1997.3.1 
[19] 
Yuncheng You. Global attractor of the GrayScott equations. Communications on Pure & Applied Analysis, 2008, 7 (4) : 947970. doi: 10.3934/cpaa.2008.7.947 
[20] 
Yirong Jiang, Nanjing Huang, Zhouchao Wei. Existence of a global attractor for fractional differential hemivariational inequalities. Discrete & Continuous Dynamical Systems  B, 2017, 22 (11) : 00. doi: 10.3934/dcdsb.2019216 
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