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Invariant measures and Statistical solutions of the globally modified Navier-Stokes equations
| 1. | Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla |
| 2. | Institut für Mathematik, Johann Wolfgang Goethe Universität, D-60054 Frankfurt am Main, Germany |
| 3. | Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla |
| [1] |
P.E. Kloeden, Pedro Marín-Rubio, José Real. Equivalence of invariant measures and stationary statistical solutions for the autonomous globally modified Navier-Stokes equations. Communications on Pure & Applied Analysis, 2009, 8 (3) : 785-802. doi: 10.3934/cpaa.2009.8.785 |
| [2] |
Pedro Marín-Rubio, Antonio M. Márquez-Durán, José Real. Pullback attractors for globally modified Navier-Stokes equations with infinite delays. Discrete & Continuous Dynamical Systems - A, 2011, 31 (3) : 779-796. doi: 10.3934/dcds.2011.31.779 |
| [3] |
P.E. Kloeden, José A. Langa, José Real. Pullback V-attractors of the 3-dimensional globally modified Navier-Stokes equations. Communications on Pure & Applied Analysis, 2007, 6 (4) : 937-955. doi: 10.3934/cpaa.2007.6.937 |
| [4] |
Fabio Ramos, Edriss S. Titi. Invariant measures for the $3$D Navier-Stokes-Voigt equations and their Navier-Stokes limit. Discrete & Continuous Dynamical Systems - A, 2010, 28 (1) : 375-403. doi: 10.3934/dcds.2010.28.375 |
| [5] |
Grzegorz Łukaszewicz. Pullback attractors and statistical solutions for 2-D Navier-Stokes equations. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 643-659. doi: 10.3934/dcdsb.2008.9.643 |
| [6] |
Julia García-Luengo, Pedro Marín-Rubio, José Real. Some new regularity results of pullback attractors for 2D Navier-Stokes equations with delays. Communications on Pure & Applied Analysis, 2015, 14 (5) : 1603-1621. doi: 10.3934/cpaa.2015.14.1603 |
| [7] |
Bo-Qing Dong, Juan Song. Global regularity and asymptotic behavior of modified Navier-Stokes equations with fractional dissipation. Discrete & Continuous Dynamical Systems - A, 2012, 32 (1) : 57-79. doi: 10.3934/dcds.2012.32.57 |
| [8] |
Vittorino Pata. On the regularity of solutions to the Navier-Stokes equations. Communications on Pure & Applied Analysis, 2012, 11 (2) : 747-761. doi: 10.3934/cpaa.2012.11.747 |
| [9] |
Pedro Marín-Rubio, Antonio M. Márquez-Durán, José Real. Three dimensional system of globally modified Navier-Stokes equations with infinite delays. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 655-673. doi: 10.3934/dcdsb.2010.14.655 |
| [10] |
G. Deugoué, T. Tachim Medjo. The Stochastic 3D globally modified Navier-Stokes equations: Existence, uniqueness and asymptotic behavior. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2593-2621. doi: 10.3934/cpaa.2018123 |
| [11] |
Peter Constantin, Gregory Seregin. Global regularity of solutions of coupled Navier-Stokes equations and nonlinear Fokker Planck equations. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1185-1196. doi: 10.3934/dcds.2010.26.1185 |
| [12] |
Daoyuan Fang, Bin Han, Matthias Hieber. Local and global existence results for the Navier-Stokes equations in the rotational framework. Communications on Pure & Applied Analysis, 2015, 14 (2) : 609-622. doi: 10.3934/cpaa.2015.14.609 |
| [13] |
Daniel Pardo, José Valero, Ángel Giménez. Global attractors for weak solutions of the three-dimensional Navier-Stokes equations with damping. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3569-3590. doi: 10.3934/dcdsb.2018279 |
| [14] |
Zoran Grujić. Regularity of forward-in-time self-similar solutions to the 3D Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2006, 14 (4) : 837-843. doi: 10.3934/dcds.2006.14.837 |
| [15] |
Keyan Wang. On global regularity of incompressible Navier-Stokes equations in $\mathbf R^3$. Communications on Pure & Applied Analysis, 2009, 8 (3) : 1067-1072. doi: 10.3934/cpaa.2009.8.1067 |
| [16] |
Susan Friedlander, Nataša Pavlović. Remarks concerning modified Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 269-288. doi: 10.3934/dcds.2004.10.269 |
| [17] |
Yukang Chen, Changhua Wei. Partial regularity of solutions to the fractional Navier-Stokes equations. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5309-5322. doi: 10.3934/dcds.2016033 |
| [18] |
Joanna Rencławowicz, Wojciech M. Zajączkowski. Global regular solutions to the Navier-Stokes equations with large flux. Conference Publications, 2011, 2011 (Special) : 1234-1243. doi: 10.3934/proc.2011.2011.1234 |
| [19] |
Peixin Zhang, Jianwen Zhang, Junning Zhao. On the global existence of classical solutions for compressible Navier-Stokes equations with vacuum. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 1085-1103. doi: 10.3934/dcds.2016.36.1085 |
| [20] |
Reinhard Racke, Jürgen Saal. Hyperbolic Navier-Stokes equations II: Global existence of small solutions. Evolution Equations & Control Theory, 2012, 1 (1) : 217-234. doi: 10.3934/eect.2012.1.217 |
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