Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (5): 1445-1464.
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Received:
2019-07-24
Online:
2021-10-26
Published:
2021-10-08
Contact:
Xin Liu
E-mail:xinliu120@suibe.edu.cn;xld0908@163.com
Supported by:
CLC Number:
Xin Liu,Xiaolei Dong. Low Mach Number Limit to One-Dimensional Non-Isentropic Compressible Viscous Micropolar Fluid Model[J].Acta mathematica scientia,Series A, 2021, 41(5): 1445-1464.
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1 | Alazard T . Incompressible limit of the nonisentropic euler equations with the solid wall boundary conditions. Adv Differential Equations, 2005, 10, 19- 44 |
2 |
Alazard T . Low Mach number limit of the full Navier-Stokes equations. Arch Ration Mech Anal, 2006, 180, 1- 73
doi: 10.1007/s00205-005-0393-2 |
3 |
Atkinson F , Peletier L . Similarity solutions of the nonlinear diffusion equation. Arch Ration Mech Anal, 1974, 54, 373- 392
doi: 10.1007/BF00249197 |
4 | Chen M , Xu X , Zhang J . The zero limits of angular and micro-rotational viscosities for the two-dimensional micropolar fluid equations with boundary effect. Z Angew Math Phys, 2014, 65 (2): 687- 710 |
5 |
Danchin R . Low Mach number limit for viscous compressible flows. ESAIM Math Model Numer Anal, 2005, 39, 459- 475
doi: 10.1051/m2an:2005019 |
6 |
Dou C , Jiang S , Ou Y . Low Mach number limit of full Navier-Stokes equations in a 3D bounded domain. J Differential Equations, 2015, 258, 379- 398
doi: 10.1016/j.jde.2014.09.017 |
7 | Duan R . Global solutions for a one-dimensional compressible micropolar fluid model with zero heat conductivity. J Math Anal Appl, 2018, 463, 417- 495 |
8 | Eringen C A . Linear theory of micropolar elasticity. J Math Mech, 1966, 15, 909- 923 |
9 | Eringen C A . Theory of micropolar fluids. J Math Mech, 1966, 16, 1- 16 |
10 | Feireisl E , Novotny A . Singular Limits in Thermodynamics of Viscous Fluids. Basel: Birkhäuser, 2009 |
11 |
Fan J , Gao H , Guo B . Low Mach number limit of the compressible magnetohydrodynamic equations with zero thermal conductivity coefficient. Math Methods Appl Sci, 2011, 34, 2181- 2188
doi: 10.1002/mma.1515 |
12 |
Hu X , Wang D . Low Mach number limit of viscous compressible magnetohydrodynamic flows. SIAM J Math Anal, 2009, 41, 1272- 1294
doi: 10.1137/080723983 |
13 |
Huang F , Wang T , Wang Y . Diffusive wave in the low Mach limit for compressible Navier-Stokes equations. Adv Math, 2017, 319, 348- 395
doi: 10.1016/j.aim.2017.08.004 |
14 |
Jiang S , Ju Q , Li F . Incompressible limit of the compressible magnetohydrodynamic equations with vanishing viscosity coefficients. SIAM J Math Anal, 2010, 42, 2539- 2553
doi: 10.1137/100785168 |
15 |
Jiang S , Ou Y . Incompressible limit of the non-isentropic Navier-Stokes equations with well-prepared initial data in three-dimensional bounded domains. J Math Pures Appl, 2011, 96, 1- 28
doi: 10.1016/j.matpur.2011.01.004 |
16 | Jiang S , Ju Q , Li F . Low Mach number limit for the multi-dimensional full magnetohydrodynamic equations. Nonlinearity, 2012, 15, 1351- 1365 |
17 |
Jiang S , Ju Q , Li F . Incompressible limit of the non-isentropic ideal magnetohydrodynamic equations. SIAM J Math Anal, 2016, 48 (1): 302- 319
doi: 10.1137/15M102842X |
18 |
Jiang S , Ju Q , Li F , Xin Z . Low Mach number limit for the full compressible magnetohydrodynamic equations with general initial data. Adv Math, 2014, 259, 384- 420
doi: 10.1016/j.aim.2014.03.022 |
19 |
Kim H , Lee J . The incompressible limits of viscous polytropic fluids with zero thermal conductivity coefficient. Comm Partial Differential Equations, 2005, 30, 1169- 1189
doi: 10.1080/03605300500257560 |
20 |
Klainerman S , Majda A . Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Comm Pure Appl Math, 1981, 34, 481- 524
doi: 10.1002/cpa.3160340405 |
21 |
Klainerman S , Majda A . Compressible and incompressible fluids. Comm Pure Appl Math, 1982, 35, 629- 653
doi: 10.1002/cpa.3160350503 |
22 |
Levermore C , Sun W , Trivisa K . A low Mach number limit of a dispersive Navier-Stokes system. SIAM J Math Anal, 2012, 44, 1760- 1807
doi: 10.1137/100818765 |
23 |
Li Y . Convergence of the compressible magnetohydrodynamic equations to incompressible magnetohydrodynamic equations. J Differential Equations, 2012, 252, 2725- 2738
doi: 10.1016/j.jde.2011.10.002 |
24 |
Liu Q , Yin H . Stability of contact discontinuity for 1-D compressible viscous micropolar fluid model. Nonlinear Anal, 2017, 149, 41- 55
doi: 10.1016/j.na.2016.10.009 |
25 |
Liu Q , Zhang P . Optimal time decay of the compressible micropolar fluids. J Differential Equations, 2016, 260, 7634- 7664
doi: 10.1016/j.jde.2016.01.037 |
26 |
Liu Y . Diffusive wave in the low Mach limit for non-viscous and heat-conductive gas. J Differential Equations, 2018, 264, 6933- 6958
doi: 10.1016/j.jde.2018.02.003 |
27 | Masmoudi N . Examples of singular limits in hydrodynamics. Handbook of Differential Equations: Evolutionary Equations, 2007, 3, 195- 275 |
28 |
Métivier G , Schochet S . The incompressible limit of the non-isentropic Eulere quations. Arch Ration Mech Anal, 2001, 158, 61- 90
doi: 10.1007/PL00004241 |
29 |
Métivier G , Schochet S . Averaging theorems for conservative systems and the weakly compressible Euler equations. J Differential Equations, 2003, 187, 106- 183
doi: 10.1016/S0022-0396(02)00037-2 |
30 |
Schochet S . The compressible Euler equations in a bounded domain: existence of solutions and the incompressible limit. Comm Math Phys, 1986, 104, 49- 75
doi: 10.1007/BF01210792 |
31 | Schochet S. The mathematical theory of the incompressible limit in fluid dynamics// Friedlander S, Serre D. Handbook of Mathematical Fluid Dynamics. Vol Ⅳ. Amsterdam: Elsevier, 2007 |
32 |
Su J . Incompressible limit of a compressible micropolar fluid model with general initial data. Nonlinear Anal, 2016, 132, 1- 24
doi: 10.1016/j.na.2015.10.020 |
33 |
Su J . Low Mach number limit of a compressible micropolar fluid model. Nonlinear Anal RWA, 2017, 38, 21- 34
doi: 10.1016/j.nonrwa.2017.04.005 |
34 | Ukai S . The incompressible limit and the initial layer of the compressible Euler equation. J Math Kyoto Univ, 1986, 26, 323- 331 |
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