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Abstrakty
In this article,we study a coupled Allen-Cahn-Navier-Stokes model in a two-dimensional domain. The model consists of the Navier-Stokes equations for the velocity, coupled with an Allen-Cahn model for the order (phase) parameter.We present an equivalent weak formulation for the model, and we prove a new regularity result for the weak solutions.
Wydawca
Czasopismo
Rocznik
Tom
Strony
111--117
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
- Department of Mathematics and Statistics, Florida International University, MMC, Miami, Florida 33199, USA
Bibliografia
- [1] H. Abels, On a diffuse interface model for two-phase flows of viscous, incompressible fluids with matched densities, Arch. Ration. Mech. Anal. 194 (2009), no. 2, 463-506.
- [2] H. Abels and E. Feireisl, On a diffuse interface model for a two-phase flow of compressible viscous fluids, Indiana Univ. Math. J. 57 (2008), no. 2, 659-698.
- [3] T. Blesgen, A generalization of the Navier-Stokes equation to two-phase flow, Phys. D 32 (1999), 1119-1123.
- [4] G. Caginalp, An analysis of a phase field model of a free boundary, Arch. Ration. Mech. Anal. 92 (1986), no. 3, 205-245.
- [5] 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), no. 7, 1129-1160.
- [6] 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), no. 1, 401-436.
- [7] C. G. Gal and M. Grasselli, Longtime behavior for a model of homogeneous incompressible two-phase flows, Discrete Contin. Dyn. Syst. 28 (2010), no. 1, 1-39.
- [8] C. G. Gal and M. Grasselli, Trajectory attractors for binary fluid mixtures in 3D, Chin. Ann. Math. Ser. B 31 (2010), no. 5, 655-678.
- [9] M. E. Gurtin, D. Polignone and J. Viñals, Two-phase binary fluids and immiscible fluids described by an order parameter, Math. Models Methods Appl. Sci. 6 (1996), no. 6, 815-831.
- [10] P. C. Hohenberg and B. I. Halperin, Theory of dynamical critical phenomena, Rev. Modern Phys. 49 (1977), 435-479.
- [11] A. Onuki, Phase transition of fluids in shear flow, J. Phys. Condens. Matter 9 (1997), 6119-6157.
- [12] T. Tachim Medjo, A non-autonomous two-phase flow model with oscillating external force and its global attractor, Nonlinear Anal. 75 (2012), no. 1, 226-243.
- [13] T. Tachim Medjo, Pullback attractors for a non-autonomous homogeneous two-phase flow model, J. Differential Equations 253 (2012), no. 6, 1779-1806.
- [14] T. Tachim-Medjo, Optimal control of a two-phase flow model with state constraints, Math. Control Relat. Fields 6 (2016), no. 2, 335-362.
- [15] T. Tachim Medjo and F. Tone, Long time stability of a classical efficient scheme for an incompressible two-phase flow model, Asymptot. Anal. 95 (2015), no. 1-2, 101-127.
- [16] R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, 2nd ed., Appl. Math. Sci. 68, Springer, New York, 1997.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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