Stability of stationary for inflow problem on the coupled compressible Navier–Stokes/Allen–Cahn system

References

• Blesgen T. A generalization of the Navier–Stokes equations to two-phase flows. J Phys D Appl Phys. 1999;32:1119–1123.
   Web of Science ®Google Scholar
• Freistúhler H, Kotschote M. Phase-field and Korteweg-type models for the time-dependent flow of compressible two-phase fluids. Arch Rational Mech Anal. 2017;224:1–20.
   Web of Science ®Google Scholar
• Feireisl E, Petzeltová H, Rocca E, et al. Analysis of a phase-field model for two-phase compressible fluids. Math Models Methods Appl Sci. 2010;20:1129–1160.
   Web of Science ®Google Scholar
• Kotschote M. Spectral analysis for travelling waves in compressible two-phase fluids of Navier–Stokes-Allen–Cahn type. J Evol Equ. 2017;17:359–385.
   Web of Science ®Google Scholar
• Luo T, Yin HY, Zhu CJ. Stability of composite wave for compressible Navier–Stokes/Allen–Cahn system. Math Models Methods Appl Sci. 2019;30:343–385.
   Web of Science ®Google Scholar
• Matsumura A. Inflow and outflow problems in the half space for a one-dimensional isentropic model system of compressible viscous gas. Methods Appl Anal. 2001;8:645:666.
   Google Scholar
• Nakamura T, Nishibata S. Stationary wave associated with an inflow problem in the half line for viscous heat-conductive gas. J Hyperbolic Differ Equ. 2011;8:651–670.
   Web of Science ®Google Scholar
• Qin XH, Wang Y. Stability of wave patterns to the inflow problem of full compressible Navier–Stokes equations. SIAM J Math Anal. 2009;41:2057–2087.
   Web of Science ®Google Scholar
• Yin HY. Stability of stationary solutions for inflow problem on the planar magnetohydrodynamics. J Math Phys. 2018. 59. 023101. 15 pp.
   Google Scholar
• Gal CG, Grasselli M. Asymptotic behavior of a Cahn-Hilliard-Navier–Stokes system in 2D. Ann Inst H Poincarè Anal Non Linèaire. 2010;27:401–436.
   Web of Science ®Google Scholar
• Xu X, Zhao LY, Liu C. Axisymmetric solutions to coupled Navier–Stokes/Allen–Cahn equations. SIAM J Math Anal. 2009;41:2246–2282.
   Web of Science ®Google Scholar
• Kotschote M. Strong solutions of the Navier–Stokes equations for a compressible fluid of Allen–Cahn type. Arch Ration Mech Anal2012;206:489–514.
   Web of Science ®Google Scholar
• Zhao LY, Guo BL, Huang HY. Vanishing viscosity limit for a coupled Navier–Stokes/Allen–Cahn system. J Math Anal Appl. 2011;384:232–245.
   Web of Science ®Google Scholar
• Ding SJ, Li YH, Luo WL. Global solutions for a coupled compressible Navier–Stokes/Allen–Cahn system in 1D. J Math Fluid Mech. 2013;15:335–360.
   Web of Science ®Google Scholar
• Chen MT, Guo XW. Global large solutions for a coupled compressible Navier–Stokes/Allen–Cahn system with initial vacuum. Nonlinear Anal Real World Appl. 2017;37:350–373.
   Web of Science ®Google Scholar
• Boyer F. A theoretical and numerical model for the study of incompressible mixture flows. Comput Fluids. 2002;31:41–68.
   Web of Science ®Google Scholar
• Liu WY, Bertozzi A, Kolokolnikov T. Diffuse interface surface tension models in an expanding flow. Commun Math Sci. 2012;10:387–418.
   Web of Science ®Google Scholar
• Yang XF, Feng JJ, Liu C, Shen J. Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method. J Comput Phys. 2006;218:417–428.
   Web of Science ®Google Scholar
• Evje S, Wen HY. On the large time behavior of the compressible gas-liquid drift-flux model with slip. Math Models Methods Appl Sci. 2015;25:2175–2215.
   Web of Science ®Google Scholar
• Evje S, Wen HY. Global solutions of a viscous gas-liquid model with unequal fluid velocities in a closed conduit. SIAM J Math Anal. 2015;47:381–406.
   Web of Science ®Google Scholar
• Evje S, Wen HY. Weak solutions of a two-phase Navier–Stokes model with a general slip law. J Funct Anal. 2015;268:93–139.
   Web of Science ®Google Scholar
• Fan LL, Liu HX, Wang T, Zhao HJ. Inflow problem for the one-dimensional compressible Navier–Stokes equations under large initial perturbation. J Differ Equ. 2014;257:3521–3553.
   Web of Science ®Google Scholar
• Kawashima S, Nishibata S, Zhu PC. Asymptotic stability of the stationary solution to the compressible Navier–Stokes equations in the half space. Comm Math Phys. 2003;240:483–500.
   Web of Science ®Google Scholar
• Matsumura A, Nishihara K. Large-time behaviors of solutions to an inflow problem in the half space for a one-dimensional system of compressible viscous gas. Commun Math Phys. 2001;222:449:474.
   Web of Science ®Google Scholar
• Nakamura T, Nishibata S, Yuge T. Convergence rate of solutions toward stationary solutions to the compressible Navier–Stokes equation in a half line. J Differ Equ. 2007;241:94–111.
   Web of Science ®Google Scholar
• Qin XH. Large-time behaviour of solutions to the outflow problem of full compressible Navier–Stokes equations. Nonlinearity. 2011;24:1369–1394.
   Web of Science ®Google Scholar
• Qin XH, Wang Y. Large-time behavior of solutions to the inflow problem of full compressible Navier–Stokes equations. SIAM J Math Anal. 2011;43:341–366.
   Web of Science ®Google Scholar
• Wan L, Wang T, Zhao HJ. Asymptotic stability of wave patterns to compressible viscous and heat-conducting gases in the half-space. J Differ Equ. 2016;261:5949 17.
   Web of Science ®Google Scholar
• Wan L, Wang T, Zou QY. Stability of stationary solutions to the outflow problem for full compressible Navier–Stokes equations with large initial perturbation. Nonlinearity. 2016;29:1329–1354.
   Web of Science ®Google Scholar
• Duan RJ, Yang XF, Stability of rarefaction wave and boundary layer for outflow problem on the two-fluid Navier–Stokes-Poisson equations. Comm Pure Appl Anal. 2013; 12:985–1014.
   Web of Science ®Google Scholar
• Nikkuni Y, Kawashima S. Stability of stationary solutions to the half-space problem for the discrete Boltzmann equation with multiple collisions. Kyushu J Math. 2000;54233–255.
   Google Scholar
• Yin HY, Wang T, Zou QY. Stability of stationary solutions for inflow problem on the micropolar fluid model. Z Angew Math Phys. 2017;68:13 pp .
   Web of Science ®Google Scholar