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On a class of three dimensional Navier-Stokes equations with bounded delay
1. | Universidade Estadual do Oeste do Paraná - UNIOESTE, Colegiado do curso de Matemática, Rua Universitária, 2069. Cx.P. 711, 85819-110 Cascavel, PR, Brazil |
2. | Departamento de Matemática, IMECC - UNICAMP, Rua Sergio Buarque de Holanda, 651, 13083-859 Campinas, SP, Brazil |
References:
[1] |
T. Caraballo and J. Real, Navier-Stokes equations with delays, Proc. R. Soc. Lond. A, 457 (2001), 2441-2453.
doi: 10.1098/rspa.2001.0807. |
[2] |
T. Caraballo and J. Real, Asymptotic behavior of two-dimensional Navier-Stokes equations with delays, Proc. R. Soc. Lond. A, 459 (2003), 3181-3194.
doi: 10.1098/rspa.2003.1166. |
[3] |
T. Caraballo and J. Real, Attractors for 2D-Navier-Stokes models with delays, J. Differential Equations, 205 (2004), 271-297.
doi: 10.1016/j.jde.2004.04.012. |
[4] |
M. J. Garrido-Atienza and P. Marín-Rubio, Navier-Stokes equations with delays on unbounded domains, Nonlinear Anal., 64 (2006), 1100-1118.
doi: 10.1016/j.na.2005.05.057. |
[5] |
W. Liu, Asymptotic behavior of solutions of time-delayed Burgers' equation, Discrete Contin. Dyn. Syst. Ser. B., 2 (2002), 47-56.
doi: 10.3934/dcdsb.2002.2.47. |
[6] |
P. Marín-Rubio and J. Real, Attractors for 2D-Navier-Stokes equations with delays on some unbounded domains, Nonlinear Anal., 67 (2007), 2784-2799.
doi: 10.1016/j.na.2006.09.035. |
[7] |
P. Marín-Rubio and J. Real, Pullback attractors for 2D-Navier-Stokes equations with delays in continuous and sub-linear operators, Discrete Contin. Dyn. Syst., 26 (2010), 989-1006.
doi: 10.3934/dcds.2010.26.989. |
[8] |
G. Planas and E. Hernández, Asymptotic behaviour of two-dimensional time-delayed Navier-Stokes equations, Discrete Contin. Dyn. Syst., 21 (2008), 1245-1258.
doi: 10.3934/dcds.2008.21.1245. |
[9] |
J. C. Robinson, "Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors," Cambridge texts in applied mathematics, Cambridge University Press, 2001. |
[10] |
Y. Tang and M. Wan, A remark on exponential stability of time-delayed Burgers equation, Discrete Contin. Dyn. Syst. Ser. B., 12 (2009), 219-225.
doi: 10.3934/dcdsb.2009.12.219. |
[11] |
T. Taniguchi, The exponential behavior of Navier-Stokes equations with time delay external force, Discrete Contin. Dyn. Syst., 12 (2005), 997-1018.
doi: 10.3934/dcds.2005.12.997. |
[12] |
R. Temam, "Navier-Stokes Equations: Theory and Numerical Analysis," Studies in Mathematics and its applications. Volume 2, The Netherlands, 1984. |
show all references
References:
[1] |
T. Caraballo and J. Real, Navier-Stokes equations with delays, Proc. R. Soc. Lond. A, 457 (2001), 2441-2453.
doi: 10.1098/rspa.2001.0807. |
[2] |
T. Caraballo and J. Real, Asymptotic behavior of two-dimensional Navier-Stokes equations with delays, Proc. R. Soc. Lond. A, 459 (2003), 3181-3194.
doi: 10.1098/rspa.2003.1166. |
[3] |
T. Caraballo and J. Real, Attractors for 2D-Navier-Stokes models with delays, J. Differential Equations, 205 (2004), 271-297.
doi: 10.1016/j.jde.2004.04.012. |
[4] |
M. J. Garrido-Atienza and P. Marín-Rubio, Navier-Stokes equations with delays on unbounded domains, Nonlinear Anal., 64 (2006), 1100-1118.
doi: 10.1016/j.na.2005.05.057. |
[5] |
W. Liu, Asymptotic behavior of solutions of time-delayed Burgers' equation, Discrete Contin. Dyn. Syst. Ser. B., 2 (2002), 47-56.
doi: 10.3934/dcdsb.2002.2.47. |
[6] |
P. Marín-Rubio and J. Real, Attractors for 2D-Navier-Stokes equations with delays on some unbounded domains, Nonlinear Anal., 67 (2007), 2784-2799.
doi: 10.1016/j.na.2006.09.035. |
[7] |
P. Marín-Rubio and J. Real, Pullback attractors for 2D-Navier-Stokes equations with delays in continuous and sub-linear operators, Discrete Contin. Dyn. Syst., 26 (2010), 989-1006.
doi: 10.3934/dcds.2010.26.989. |
[8] |
G. Planas and E. Hernández, Asymptotic behaviour of two-dimensional time-delayed Navier-Stokes equations, Discrete Contin. Dyn. Syst., 21 (2008), 1245-1258.
doi: 10.3934/dcds.2008.21.1245. |
[9] |
J. C. Robinson, "Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors," Cambridge texts in applied mathematics, Cambridge University Press, 2001. |
[10] |
Y. Tang and M. Wan, A remark on exponential stability of time-delayed Burgers equation, Discrete Contin. Dyn. Syst. Ser. B., 12 (2009), 219-225.
doi: 10.3934/dcdsb.2009.12.219. |
[11] |
T. Taniguchi, The exponential behavior of Navier-Stokes equations with time delay external force, Discrete Contin. Dyn. Syst., 12 (2005), 997-1018.
doi: 10.3934/dcds.2005.12.997. |
[12] |
R. Temam, "Navier-Stokes Equations: Theory and Numerical Analysis," Studies in Mathematics and its applications. Volume 2, The Netherlands, 1984. |
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