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The Navier-Stokes-Cahn-Hilliard equations for mildly compressible binary fluid mixtures

  • * Corresponding author: Andrea Giorgini

    * Corresponding author: Andrea Giorgini 
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  • We study the well-posedness for the mildly compressible Navier-Stokes-Cahn-Hilliard system with non-constant viscosity and Landau potential in two and three dimensional domains.

    Mathematics Subject Classification: Primary: 35Q35, 35D30, 35D35; Secondary: 76T05.

    Citation:

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  • [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), 463-506.  doi: 10.1007/s00205-008-0160-2.
    [2] H. Abels, Existence of weak solutions for a diffuse interface model for viscous, incompressible fluids with general densities, Comm. Math. Phys., 289 (2009), 45-73.  doi: 10.1007/s00220-009-0806-4.
    [3] H. Abels, Strong well-posedness of a diffuse interface model for a viscous, quasi-incompressible two-phase flow, SIAM J. Math. Anal., 44 (2012), 316-340.  doi: 10.1137/110829246.
    [4] H. AbelsD. Depner and H. Garcke, Existence of weak solutions for a diffuse interface model for two-phase flows of incompressible fluids with different densities, J. Math. Fluid Mech., 15 (2013), 453-480.  doi: 10.1007/s00021-012-0118-x.
    [5] H. Abels and E. Feireisl, On a diffuse interface model for two-phase flow of compressible viscous fluids, Indiana Univ. Math. J., 57 (2008), 659-698.  doi: 10.1512/iumj.2008.57.3391.
    [6] H. Abels, H. Garcke and G. Grün, Thermodynamically consistent, frame indifferent diffuse interface models for incompressible two-phase flows with different densities, Math. Models Methods Appl. Sci., 22 (2012), 1150013, 40 pp. doi: 10.1142/S0218202511500138.
    [7] H. Bahouri, J.-Y. Chemin and R. Danchin, Fourier Analysis and Nonlinear Partial Differential Equations, Grundlehren der Mathematischen Wissenschaften, 343. Springer, Heidelberg, 2011. doi: 10.1007/978-3-642-16830-7.
    [8] A. Bensoussan and J. Frehse, Regularity Results for Nonlinear Elliptic Systems and Applications., Applied Mathematical Sciences, 151. Springer-Verlag, Berlin, 2002. doi: 10.1007/978-3-662-12905-0.
    [9] F. Boyer, Mathematical study of multi-phase flow under shear through order parameter formulation, Asympt. Anal., 20 (1999), 175-212. 
    [10] F. Boyer, A theoretical and numerical model for the study of incompressible mixture flows, Comput. Fluids, 31 (2002), 41-68.  doi: 10.1016/S0045-7930(00)00031-1.
    [11] F. Boyer and P. Fabrie, Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models, Applied Mathematical Sciences, 183. Springer, New York, 2013. doi: 10.1007/978-1-4614-5975-0.
    [12] C. S. Cao and C. G. Gal, Global solutions for the 2D NS-CH model for a two-phase flow of viscous, incompressible fluids with mixed partial viscosity and mobility, Nonlinearity, 25 (2012), 3211-3234.  doi: 10.1088/0951-7715/25/11/3211.
    [13] L. CherfilsE. FeireislM. MichálekA. MiranvilleM. Petcu and D. Pražák, The compressible Navier-Stokes-Cahn-Hilliard equations with dynamic boundary conditions, Math. Models Methods Appl. Sci., 29 (2019), 2557-2584.  doi: 10.1142/S0218202519500544.
    [14] F. Demengel and G. Demengel, Functional Spaces for the Theory of Elliptic Partial Differential Equations, Universitext. Springer, London, EDP Sciences, Les Ulis, 2012. doi: 10.1007/978-1-4471-2807-6.
    [15] H. DingP. D. M. Spelt and C. Shu, Diffuse interface model for incompressible two-phase flows with large density ratios, J. Comput. Phys., 226 (2007), 2078-2095. 
    [16] C. G. Gal and M. Grasselli, Asymptotic behavior of a Cahn-Hilliard-Navier-Stokes in 2D, Ann. Inst. H. Poincaré Anal. Non Linéaire, 27 (2010), 401-436.  doi: 10.1016/j.anihpc.2009.11.013.
    [17] C. G. Gal and M. Grasselli, Trajectory attractors for binary fluid mixtures in 3D, Chinese Ann. Math. Ser. B, 31 (2010), 655-678.  doi: 10.1007/s11401-010-0603-6.
    [18] C. G. Gal, M. Grasselli and A. Miranville, Cahn-Hilliard-Navier-Stokes systems with moving contact lines, Calc. Var. Partial Differential Equations, 55 (2016), Art. 50, 47 pp. doi: 10.1007/s00526-016-0992-9.
    [19] C. G. GalM. Grasselli and H. Wu, Global weak solutions to a diffuse interface model for incompressible two-phase flows with moving contact lines and different densities, Arch. Ration. Mech. Anal., 234 (2019), 1-56.  doi: 10.1007/s00205-019-01383-8.
    [20] M.-H. Giga, A. Kirshtein and C. Liu, Variational modeling and complex fluids, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, Springer, Cham, (2018), 73–113. doi: 10.1007/978-3-319-13344-7_2.
    [21] A. GiorginiA. Miranville and R. Temam, Uniqueness and regularity for the Navier-Stokes-Cahn-Hilliard system, SIAM J. Math. Anal., 51 (2019), 2535-2574.  doi: 10.1137/18M1223459.
    [22] M. E. GurtinD. Polignone and J. Viñals, Two-phase binary fluids and immiscible fluids described by an order parameter, Math. Models Methods Appl. Sci., 6 (1996), 815-831.  doi: 10.1142/S0218202596000341.
    [23] P. G. Lemarié-RieussetThe Navier-Stokes Problem in the 21st Century, CRC Press, Boca Raton, FL, 2016.  doi: 10.1201/b19556.
    [24] J.-L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications. Vol. I, Die Grundlehren der mathematischen Wissenschaften, Band 181. Springer-Verlag, New York-Heidelberg, 1972.
    [25] J. Lowengrub and L. Truskinovsky, Quasi-incompressible Cahn–Hilliard fluids and topological transitions, Proc. Roy. Soc. Lond. A, 454 (1998), 2617-2654.  doi: 10.1098/rspa.1998.0273.
    [26] V. N. Starovoĭtov, Model of the motion of a two-component liquid with allowance of capillary forces, J. Appl. Mech. Tech. Phys., 35 (1994), 891-897.  doi: 10.1007/BF02369582.
    [27] R. Temam, Infinite-dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematical Sciences, 68. Springer-Verlag, New York, 1997. doi: 10.1007/978-1-4612-0645-3.
    [28] R. Temam, Navier-Stokes Equations: Theory and Numerical Analysis, AMS Chelsea Publishing, Providence, 2001. doi: 10.1090/chel/343.
    [29] G. Tomassetti, An interpretation of Temam's stabilization term in the quasi-incompressible Navier-Stokes system, arXiv: 1909.11168.
    [30] K. E. Wardle and T. Lee, Finite element lattice Boltzmann simulations of free surface flow in a concentric cylinder, Comput. Math. Appl., 65 (2013), 230-238.  doi: 10.1016/j.camwa.2011.09.020.
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