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Invariant measures for the $3$D NavierStokesVoigt equations and their NavierStokes limit
1.  Department of Computer Science and Applied Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel, Israel 
[1] 
Luigi C. Berselli, TaeYeon Kim, Leo G. Rebholz. Analysis of a reducedorder approximate deconvolution model and its interpretation as a NavierStokesVoigt regularization. Discrete and Continuous Dynamical Systems  B, 2016, 21 (4) : 10271050. doi: 10.3934/dcdsb.2016.21.1027 
[2] 
Gaocheng Yue, Chengkui Zhong. Attractors for autonomous and nonautonomous 3D NavierStokesVoight equations. Discrete and Continuous Dynamical Systems  B, 2011, 16 (3) : 9851002. doi: 10.3934/dcdsb.2011.16.985 
[3] 
Varga K. Kalantarov, Edriss S. Titi. Global stabilization of the NavierStokesVoight and the damped nonlinear wave equations by finite number of feedback controllers. Discrete and Continuous Dynamical Systems  B, 2018, 23 (3) : 13251345. doi: 10.3934/dcdsb.2018153 
[4] 
Cung The Anh, Dang Thi Phuong Thanh, Nguyen Duong Toan. Uniform attractors of 3D NavierStokesVoigt equations with memory and singularly oscillating external forces. Evolution Equations and Control Theory, 2021, 10 (1) : 123. doi: 10.3934/eect.2020039 
[5] 
Xinguang Yang, Baowei Feng, Thales Maier de Souza, Taige Wang. Longtime dynamics for a nonautonomous NavierStokesVoigt equation in Lipschitz domains. Discrete and Continuous Dynamical Systems  B, 2019, 24 (1) : 363386. doi: 10.3934/dcdsb.2018084 
[6] 
Vu Manh Toi. Stability and stabilization for the threedimensional NavierStokesVoigt equations with unbounded variable delay. Evolution Equations and Control Theory, 2021, 10 (4) : 10071023. doi: 10.3934/eect.2020099 
[7] 
Tomás Caraballo, Peter E. Kloeden, José Real. Invariant measures and Statistical solutions of the globally modified NavierStokes equations. Discrete and Continuous Dynamical Systems  B, 2008, 10 (4) : 761781. doi: 10.3934/dcdsb.2008.10.761 
[8] 
Adam Larios, Yuan Pei. Approximate continuous data assimilation of the 2D NavierStokes equations via the Voigtregularization with observable data. Evolution Equations and Control Theory, 2020, 9 (3) : 733751. doi: 10.3934/eect.2020031 
[9] 
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 
[10] 
P.E. Kloeden, Pedro MarínRubio, José Real. Equivalence of invariant measures and stationary statistical solutions for the autonomous globally modified NavierStokes equations. Communications on Pure and Applied Analysis, 2009, 8 (3) : 785802. doi: 10.3934/cpaa.2009.8.785 
[11] 
Anne Bronzi, Ricardo Rosa. On the convergence of statistical solutions of the 3D NavierStokes$\alpha$ model as $\alpha$ vanishes. Discrete and Continuous Dynamical Systems, 2014, 34 (1) : 1949. doi: 10.3934/dcds.2014.34.19 
[12] 
Grzegorz Łukaszewicz. Pullback attractors and statistical solutions for 2D NavierStokes equations. Discrete and Continuous Dynamical Systems  B, 2008, 9 (3&4, May) : 643659. doi: 10.3934/dcdsb.2008.9.643 
[13] 
Bo You. Trajectory statistical solutions for the CahnHilliardNavierStokes system with moving contact lines. Discrete and Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021251 
[14] 
Matthew Paddick. The strong inviscid limit of the isentropic compressible NavierStokes equations with Navier boundary conditions. Discrete and Continuous Dynamical Systems, 2016, 36 (5) : 26732709. doi: 10.3934/dcds.2016.36.2673 
[15] 
Wenjing Song, Ganshan Yang. The regularization of solution for the coupled NavierStokes and Maxwell equations. Discrete and Continuous Dynamical Systems  S, 2016, 9 (6) : 21132127. doi: 10.3934/dcdss.2016087 
[16] 
Kuijie Li, Tohru Ozawa, Baoxiang Wang. Dynamical behavior for the solutions of the NavierStokes equation. Communications on Pure and Applied Analysis, 2018, 17 (4) : 15111560. doi: 10.3934/cpaa.2018073 
[17] 
Vittorino Pata. On the regularity of solutions to the NavierStokes equations. Communications on Pure and Applied Analysis, 2012, 11 (2) : 747761. doi: 10.3934/cpaa.2012.11.747 
[18] 
Tian Ma, Shouhong Wang. Asymptotic structure for solutions of the NavierStokes equations. Discrete and Continuous Dynamical Systems, 2004, 11 (1) : 189204. doi: 10.3934/dcds.2004.11.189 
[19] 
Eric Blayo, Antoine Rousseau. About interface conditions for coupling hydrostatic and nonhydrostatic NavierStokes flows. Discrete and Continuous Dynamical Systems  S, 2016, 9 (5) : 15651574. doi: 10.3934/dcdss.2016063 
[20] 
Misha Perepelitsa. An illposed problem for the NavierStokes equations for compressible flows. Discrete and Continuous Dynamical Systems, 2010, 26 (2) : 609623. doi: 10.3934/dcds.2010.26.609 
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