二维不可压缩 Navier-Stokes-Allen-Cahn 系统的边界层分离

Abstract

Abstract:

In this paper, boundary layer separation of 2-D incompressible Navier-Stokes-Allen-Cahn system is considered. Firstly, the condition of boundary layer separation under flat boundary is obtained with the help of the geometric theory of incompressible flow and Taylor expansion. Secondly, the expression for boundary singularity is presented and the condition of boundary layer separation under curved boundary is discovered. The conditions, determined by initial values and external forces, can predict when and where boundary layer separation for Navier-Stokes-Allen-Cahn system will occur.

Key words: Boundary layer separation, Navier-Stokes-Allen-Cahn system, Bifurcation, 2-D incompressible flow

CLC Number:

O175.29

Chen Min,Hu Biyan,Luo Hong. Boundary Layer Separation of 2-D Incompressible Navier-Stokes-Allen-Cahn System[J].Acta mathematica scientia,Series A, 2023, 43(4): 1123-1132.

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References

[1]	Xu X, Zhao L Y, Liu C. Axisymmetric solution to coupled Navier-Stokes/Allen-Cahn equations. SIAM Journal on Mathematical Analysis, 2009, 41(6): 2246-2282
[2]	Gal C G, Grasselli M. Longtime behavior for a model of homogeneous incompressible two-phase flows. Discrete and Continuous Dynamical Systems, 2010, 28(1): 1-39
[3]	Zhao L Y, Guo B L, Huang H Y. Vanishing viscosity limit for a coupled Navier-Stokes/Allen-Cahn system. Journal of Mathematical Analysis and Applications, 2011, 384(2): 232-245
[4]	Medjo T T. On the existence and uniqueness of solution to a stochastic $2$ D Allen-Cahn-Navier-Stokes model. Stochastics and Dynamics, 2019, 19(1): 1950007
[5]	Zhao X P. Global well-posedness and decay estimates for three-dimensional compressible Navier-Stokes-Allen-Cahn system. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 2022, 152(5): 1291-1322
[6]	Li Y H, Ding S J, Huang M X. Blow-up criterion for an incompressible Navier-Stokes-Allen-Cahn system with different densities. Discrete and Continuous Dynamical Systems, 2016, 21(5): 1507-1523
[7]	Chen M T, Guo X W. Global large solutions for a coupled compressible Navier-Stokes/Allen-Cahn system with initial vacuum. Nonlinear Analysis: Real World Applications, 2017, 37: 350-373
[8]	Li Y H, Huang M X. Strong solutions for an incompressible Navier-Stokes-Allen-Cahn system with different densities. Journal of Applied Mathematics and Physics, 2018, 69(3): 1-18
[9]	Deteix J, Kouamo G, Yakoubi D. Well-posedness of a semi-discrete Navier-Stokes-Allen-Cahn model. Journal of Mathematical Analysis and Applications, 2021, 496(2): 124816
[10]	Oleinik O. On the mathematical theory of boundary layer for unsteady flow of incompressible fluid. Journal of Applied Mathematics and Mechanics, 1966, 30(5): 951-974
[11]	Liu J G, Xin Z P. Boundary layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation. Archive for Rational Mechanics and Analysis, 1996, 135(1): 61-105
[12]	Xie X Q. Boundary layers associated with a coupled Navier-Stokes/Allen-Cahn system: the non-characteristic boundary case. Journal of Partial Differential Equations, 2012, 25(1): 66-78
[13]	FAN L L, HOU M C. Asymptotic stability of a boundary layer and rarefaction wave for the outflow problem of the heat-conductive ideal gas without viscosity. Acta Mathematica Scientia, 2020, 40B(6): 1627-1652
[14]	张浩, 汪娜. 一类弱非线性临界奇摄动积分边界问题. 数学物理学报, 2022, 42A(4): 1060-1073
[14]	Zhang H, Wang N. A class of weakly nonlinear critical singularly perturbed integral boundary problems. Acta Mathematica Scientia, 2022, 42A(4): 1060-1073
[15]	Chorin A J, Marsden J E. A Mathematical Introduction to Fluid Mechanics. New York: Springer-Verlag, 1997
[16]	Ghil M, Ma T, Wang S H. Structural bifurcation of $2$ -D incompressible flows with dirichlet boundary conditions: applications to boundary-Layer separation. SIAM Journal on Applied Mathematics, 2005, 65(5): 1576-1596
[17]	Ma T, Wang S H. Rigorous Characterization of Boundary Layer Separations. Cambridge: Proceedings Second MIT Conference on Computational Fluid and Solid Mechanics, 2003
[18]	Ghil M, Liu J G, Wang C, Wang S H. Boundary-layer separation and adverse pressure gradient for $2$ -D viscous incompressible flow. Physica D: Nonlinear Phenomena, 2004, 197(1): 149-173
[19]	Luo H, Wang Q, Ma T. A predicable condition for boundary layer separation of $2$ -D incompressible fluid flows. Nonlinear Analysis: Real World Applications, 2015, 22: 336-341
[20]	Wang Q, Luo H, Ma T. Boundary layer separation of 2-D incompressible dirichlet flows. Discrete and Continuous Dynamical Systems B, 2015, 20(2): 675-682
[21]	姜倩. 阻尼 Navier-Stokes 系统的渐近吸引子与边界层分离. 四川师范大学学报, 2020, 182(3): 96-102
[21]	Jiang Q. The asymptotic attractor of and boundary layer separtion of the damped Navier-Stokes system. Journal of Sichuan Normal University, 2020, 182(3): 96-102
[22]	Shen W M, Wang Y, Zhang Z F. Boundary layer separation and local behavior for the steady Prandtl equation. Advances in Mathematics, 2021, 389: 107896
[23]	Ma T, Wang S. Boundary layer separation and structural bifurcation for $2$ -D incompressible fluid flows. Discrete and Continuous Dynamical Systems, 2004, 10(1/2): 459-472
[24]	Ma T, Wang S H. Geometric theory of incompressible flows with applications to fluid Dynamics. Providence: American Mathematics Society, 2005

Boundary Layer Separation of 2-D Incompressible Navier-Stokes-Allen-Cahn System

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