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.

Trendmd

Figures/Tables 1

References 24

[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 doi: 10.1137/090754698
[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 doi: 10.3934/dcds.2010.28.1
[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 doi: 10.1016/j.jmaa.2011.05.042
[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 doi: 10.1016/j.nonrwa.2017.03.001
[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 doi: 10.1016/j.jmaa.2020.124816
[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 doi: 10.1016/0021-8928(66)90001-3
[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 doi: 10.1007/BF02198435
[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 doi: 10.4208/jpde
[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
	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 doi: 10.1137/S0036139903438818
[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 doi: 10.1016/j.physd.2004.06.012
[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 doi: 10.1016/j.nonrwa.2014.09.007
[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 doi: 10.3934/dcdsb.2015.20.675
[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
	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 doi: 10.1016/j.aim.2021.107896
[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 doi: 10.3934/dcdsa
[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

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

Figures/Tables 1

References 24

Related Articles 15

Metrics

Comments

Recommended 10

[1]	Rui Xu,Yan Yang. Dynamics of an HTLV-I Infection Model with Delayed and Saturated CTL Immune Response and Immune Impairment [J]. Acta mathematica scientia,Series A, 2022, 42(6): 1836-1848.
[2]	Xueli Jiang,Xuan Deng,Qiuhao Wen,Yanqin Xiong. Limit Circle Bifurcations of Polynomial Differential System with Two Parallel Switch Straight Lines [J]. Acta mathematica scientia,Series A, 2022, 42(2): 353-364.
[3]	Daoxiang Zhang,Ben Li,Dandan Chen,Yating Lin,Xinmei Wang. Hopf Bifurcation for a Fractional Differential-Algebraic Predator-Prey System with Time Delay and Economic Profit [J]. Acta mathematica scientia,Series A, 2022, 42(2): 570-582.
[4]	Yue Sun,Daoxiang Zhang,Wen Zhou. The Influence of Fear Effect on Stability Interval of Reaction-Diffusion Predator-Prey System with Time Delay [J]. Acta mathematica scientia,Series A, 2021, 41(6): 1980-1992.
[5]	Xin Xie,Jianquan Li,Yuping Wang,Dian Zhang. A Qualitative Analysis of a Tumor-Immune System with Antigenicity [J]. Acta mathematica scientia,Series A, 2021, 41(6): 1969-1979.
[6]	Bin Long,Shanshan Xu,Hui Cao,Jianquan Li. The Influence of Splitting Index on Heteroclinic Orbit Bifurcation Under Periodic Perturbation [J]. Acta mathematica scientia,Series A, 2021, 41(5): 1516-1528.
[7]	Jingnan Wang,Dezhong Yang. Stability and Bifurcation of a Pathogen-Immune Model with Delay and Diffusion Effects [J]. Acta mathematica scientia,Series A, 2021, 41(4): 1204-1217.
[8]	Leta Temesgen Desta,Wenjun Liu,Jian Ding. Dynamics of Traveling Wave Solutions to Fully Nonlinear Heavy Ion-Acoustic Degenerate Relativistic Quantum Plasmas [J]. Acta mathematica scientia,Series A, 2021, 41(2): 496-506.
[9]	Gaihui Guo,Xiaohui Liu. Hopf Bifurcation and Stability for an Autocatalytic Reversible Biochemical Reaction Model [J]. Acta mathematica scientia,Series A, 2021, 41(1): 166-177.
[10]	Mingmin Wang,Gao Jia. Bifurcation of Positive Solutions for Quasilinear Elliptic Equations with Φ-Laplacian Operator and Concave-Convex Nonlinearities [J]. Acta mathematica scientia,Series A, 2020, 40(5): 1235-1247.
[11]	Haixia Li. Existence and Uniqueness of Positive Solutions to an Unstirred Chemostat with Toxins [J]. Acta mathematica scientia,Series A, 2020, 40(5): 1175-1185.
[12]	Wang Lingjun, Wang Qiusi. Small-Amplitude Solitary Interfacial Traveling Waves in a Gravity-Capillary Two-Layered Fluid with Vorticity [J]. Acta mathematica scientia,Series A, 2020, 40(4): 947-976.
[13]	Yi Shao,Chunxiang A. Limit Cycles Bifurcations of Liénard System of Degree Four with One Nilpotent Cusp [J]. Acta mathematica scientia,Series A, 2020, 40(3): 619-630.
[14]	Xue Zhang,Yuhuai Sun. Dynamical Analysis and Traveling Wave Solutions for Generalized (3+1)-Dimensional Kadomtsev-Petviashvili Equation [J]. Acta mathematica scientia,Series A, 2019, 39(3): 501-509.
[15]	Hailong Yuan,Yuping Wang,Yanling Li. Positive Solutions of a Predator-Prey Model with Cross Diffusion [J]. Acta mathematica scientia,Series A, 2019, 39(3): 545-559.