Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

A two-phase flow model with delays
Pages: 3273 - 3294, Issue 9, November 2017

doi:10.3934/dcdsb.2017137      Abstract        References        Full text (438.7K)           Related Articles

Theodore Tachim Medjo - Department of Mathematics, Florida International University, DM413B, University Park, Miami, Florida 33199, United States (email)

1 T. Blesgen, A generalization of the Navier-Stokes equation to two-phase flow, Pysica D (Applied Physics), 32 (1999), 1119-1123.
2 G. Caginalp, An analysis of a phase field model of a free boundary, Arch. Rational Mech. Anal., 92 (1986), 205-245.       
3 T. Caraballo and X. Han, A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions, Discrete Contin. Dyn. Syst. Ser. S, 8 (2015), 1079-1101.       
4 T. Caraballo, A. M. Márquez-Durán and J. Real, Pullback and forward attractors for a 3D LANS-$\alpha$ model with delay, Discrete Contin. Dyn. Syst., 15 (2006), 559-578.       
5 T. Caraballo and J. Real, Navier-Stokes equations with delays, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 457 (2001), 2441-2453.       
6 T. Caraballo and J. Real, Asymptotic behavior of two-dimensional Navier-Stokes equations with delays, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 459 (2003), 3181-3194.       
7 T. Caraballo and J. Real, Attractors for 2D Navier-Stokes models with delays, J. Differential Equations, 205 (2004), 271-297.       
8 R. Datko, Representation of solutions and stability of linear differential-difference equations in a Banach space, J. Differential Equations, 29 (1978), 105-166.       
9 E. Feireisl, H. Petzeltová, E. Rocca and G. Schimperna, Analysis of a phase-field model for two-phase compressible fluids, Math. Models Methods Appl. Sci., 20 (2010), 1129-1160.       
10 C. G. Gal and M. Grasselli, Asymptotic behavior of a Cahn-Hilliard-Navier-Stokes system in 2D, Ann. Inst. H. Poincaré Anal. Non Linéaire, 27 (2010), 401-436.       
11 C. G. Gal and M. Grasselli, Longtime behavior for a model of homogeneous incompressible two-phase flows, Discrete Contin. Dyn. Syst., 28 (2010), 1-39.       
12 C. G. Gal and M. Grasselli, Trajectory attractors for binary fluid mixtures in 3D, Chin. Ann. Math. Ser. B, 31 (2010), 655-678.       
13 P.C. Hohenberg and B. I. Halperin, Theory of dynamical critical phenomena, Rev. Modern Phys., 49 (1977), 435-479.
14 T. Tachim Medjo, Pullback attractors for a non-autonomous homogeneous two-phase flow model, J. Diff. Equa., 253 (2012), 1779-1806.       
15 H. Mei, G. Yin and F. Wu, Properties of stochastic integro-differential equations with infinite delay: regularity, ergodicity, weak sense Fokker-Planck equations, Stochastic Process. Appl., 126 (2016), 3102-3123.       
16 S. A. Messaoudi, A. Fareh and N. Doudi, Well posedness and exponential stability in a wave equation with a strong damping and a strong delay, J. Math. Phys., 57 (2016), 111501, 13 pp.       
17 C. Niche and G. Planas, Existence and decay of solutions in full space to Navier-Stokes equations with delays, Nonlinear Anal., 74 (2011), 244-256.       
18 A. Onuki, Phase transition of fluids in shear flow, J. Phys. Condens. Matter, 9 (1997), 6119-6157.
19 T. tachim Medjo, Attractors for a two-phase flow model with delays, Differential Integral Equations, 29 (2016), 1071-1092.       
20 T. Taniguchi, The exponential behavior of Navier-Stokes equations with time delay external force, Discrete Contin. Dyn. Syst., 12 (2005), 997-1018.       
21 R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, volume 68. Appl. Math. Sci., Springer-Verlag, New York, second edition, 1997.       
22 X. S. Wang and J. Wu, Seasonal migration dynamics: periodicity, transition delay and finite-dimensional reduction, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 468 (2012), 634-650.       

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