-
Previous Article
Asymptotic stability of stationary solutions for magnetohydrodynamic equations
- DCDS Home
- This Issue
-
Next Article
Topological conjugacy of linear systems on Lie groups
Global existence and low Mach number limit to a 3D compressible micropolar fluids model in a bounded domain
Department of Mathematics, Nanjing University, Nanjing 210093, China |
This paper is devoted to investigating the global existence of strong solutions to the three-dimensional compressible micropolar fluids model in a bounded domain with small initial data. Furthermore, we present the low Mach number limit to the corresponding problem.
References:
[1] |
M. Chen,
Blow-up criterion for viscous, compressible micropolar fluids with vacuum, Nonlinear Anal. Real World Appl., 13 (2012), 850-859.
doi: 10.1016/j.nonrwa.2011.08.021. |
[2] |
M. Chen, B. Huang and J. Zhang,
Blow-up criterion for the three-dimensional equations of compressible viscous micropolar fluids with vacuum, Nonlinear Anal., 79 (2013), 1-11.
doi: 10.1016/j.na.2012.10.013. |
[3] |
M. Chen,
Global well-posedness of the 2D incompressible micropolar fluid flows with partial viscosity and angular viscosity, Acta Math. Sci. Ser. B Engl. Ed., 33 (2013), 929-935.
doi: 10.1016/S0252-9602(13)60051-X. |
[4] |
M. Chen, X. Xu and J. Zhang,
The zero limits of angular and micro-rotational viscosities for the two-dimensional micropolar fluid equations with boundary effect, Z. Angew. Math. Phys., 65 (2014), 687-710.
doi: 10.1007/s00033-013-0345-x. |
[5] |
C. Dou, S. Jiang and Y. Ou,
Low Mach number limit of full Navier-Stokes equations in a 3D bounded domain, J. Differential Equations, 258 (2015), 379-398.
doi: 10.1016/j.jde.2014.09.017. |
[6] |
C. Dou, S. Jiang and Q. Ju,
Global existence and the low Mach number limit for the compressible magnetohydrodynamic equations in a bounded domain with perfectly conducting boundary, Z. Angew. Math. Phys., 64 (2013), 1661-1678.
doi: 10.1007/s00033-013-0311-7. |
[7] |
I. Dravić, N. Mujaković, 3-D flow of a compressible viscous micropolar fluid with spherical symmetry: a local existence theorem, Bound. Value Probl. , 2012 (2012), 25pp.
doi: 10.1186/1687-2770-2012-69. |
[8] |
I. Dra$\mathbf{v}$ić and N. Mujaković,
3-D flow of a compressible viscous micropolar fluid with spherical symmetry: Large time behavior of the solution, J. Math. Anal. Appl., 431 (2015), 545-568.
doi: 10.1016/j.jmaa.2015.06.002. |
[9] |
A. C. Eringen,
Theory of micropolar fluids, J. Math. Mech., 16 (1966), 1-18.
|
[10] |
J. Fan, H. Gao and B. Guo,
Low Mach number limit of the compressible magnetohydrodynamic equations with zero thermal conductivity coefficient, Math. Methods Appl. Sci., 34 (2011), 2181-2188.
doi: 10.1002/mma.1515. |
[11] |
J. Fan, F. Li and G. Nakamura,
Uniform well-posedness and singular limits of the isentropic Navier-Stokes-Maxwell system in a bounded domain, Z. Angew. Math. Phys., 66 (2015), 1581-1593.
doi: 10.1007/s00033-014-0484-8. |
[12] |
J. Fan, F. Li and G. Nakamura, Global existence and low Mach number limit to the 3D compressible magnetohydrodynamic equations in a bounded domain, Dynamical Systems, Differential equations and Applications, Proc. of 10th AIMS Conference, (2015), 387–394.
doi: 10.3934/proc.2015.0387. |
[13] |
E. Feireisl and A. Novotný,
The low Mach number limit for the full Navier-Stokes-Fourier system, Arch. Ration. Mech. Anal., 186 (2007), 77-107.
doi: 10.1007/s00205-007-0066-4. |
[14] |
I. Fërste,
On the theory of micropolar fluids, Adv. in Mech., 2 (1979), 81-100.
|
[15] |
P. Galdi and S. Rionero,
A note on the existence and uniqueness of the micropolar fluid equations, Int. J. Eng. Sci., 15 (1977), 105-108.
doi: 10.1016/0020-7225(77)90025-8. |
[16] |
X. Hu and D. Wang,
Low Mach number limit of viscous compressible magnetohydrodynamic flows, SIAM J. Math. Anal., 41 (2009), 1272-1294.
doi: 10.1137/080723983. |
[17] |
S. Jiang, Q. Ju and F. Li,
Low Mach limits for the multi-dimensional full Magnetohydrodynamic equations, Nonlinearity, 25 (2012), 1351-1365.
doi: 10.1088/0951-7715/25/5/1351. |
[18] |
S. Jiang, Q. Ju, F. Li and Z. Xin,
Low Mach numberlimit for the full compressible magnetohydrodynamic equations with general initial data, Adv. Math., 259 (2014), 384-420.
doi: 10.1016/j.aim.2014.03.022. |
[19] |
H. Lange,
The existence of instationary flows of incompressible micropolar fluids, Arch. Mech., 29 (1977), 741-744.
|
[20] |
F. Li and Y. Mu,
Low Mach limits of the full compressible Navier-Stokes-Maxwell system, J. Math. Anal. Appl., 412 (2014), 334-344.
doi: 10.1016/j.jmaa.2013.10.064. |
[21] |
P. L. Lions,
Mathematical Topics in Fluid Mechanics, Vol. 2 Compressible Models, Oxford University Press, New York, 1998. |
[22] |
G. Łukaszewicz,
Long time behavior of 2D micropolar fluid flows, Math. Comput. Model., 34 (2001), 487-509.
doi: 10.1016/S0895-7177(01)00078-4. |
[23] |
G. Łukaszewicz,
Asymptotic behavior of micropolar fluid flows, Int. J. Eng. Sci., 41 (2003), 259-269.
doi: 10.1016/S0020-7225(02)00208-2. |
[24] |
G. Łukaszewicz,
Micropolar Fluids. Theory and Applications, Birkhäuser, Boston, 1999.
doi: 10.1007/978-1-4612-0641-5. |
[25] |
G. Lukaszewicz, M. Rojas-Medar and M. Santos,
Stationary micropolar fluid with boundary data in $L^2$, J. Math. Anal. Appl., 271 (2002), 91-107.
doi: 10.1016/S0022-247X(02)00100-2. |
[26] |
M. A. Rojas-Medar,
Magneto-Micropolar fluid motion: Existence and uniqueness of strong solution, Math. Nachr., 188 (1997), 301-319.
doi: 10.1002/mana.19971880116. |
[27] |
F. V. Silva,
Leray's problem for a viscous incompressible micropolar fluid, J. Math. Anal. Appl., 306 (2005), 692-713.
doi: 10.1016/j.jmaa.2004.10.007. |
[28] |
J. Su,
Incompressible limit of a compressible micropolar fluid model with general initial data, Nonlinear Anal., 132 (2016), 1-24.
doi: 10.1016/j.na.2015.10.020. |
[29] |
J. Su, Low Mach number limit of a compressible micropolar fluid model,
(submitted). |
[30] |
X. Yang,
Low Mach number limit of the compressible Hall-magnetohydrodynamic system, Nonlinear Anal. Real World Appl., 25 (2015), 118-126.
doi: 10.1016/j.nonrwa.2015.03.007. |
show all references
References:
[1] |
M. Chen,
Blow-up criterion for viscous, compressible micropolar fluids with vacuum, Nonlinear Anal. Real World Appl., 13 (2012), 850-859.
doi: 10.1016/j.nonrwa.2011.08.021. |
[2] |
M. Chen, B. Huang and J. Zhang,
Blow-up criterion for the three-dimensional equations of compressible viscous micropolar fluids with vacuum, Nonlinear Anal., 79 (2013), 1-11.
doi: 10.1016/j.na.2012.10.013. |
[3] |
M. Chen,
Global well-posedness of the 2D incompressible micropolar fluid flows with partial viscosity and angular viscosity, Acta Math. Sci. Ser. B Engl. Ed., 33 (2013), 929-935.
doi: 10.1016/S0252-9602(13)60051-X. |
[4] |
M. Chen, X. Xu and J. Zhang,
The zero limits of angular and micro-rotational viscosities for the two-dimensional micropolar fluid equations with boundary effect, Z. Angew. Math. Phys., 65 (2014), 687-710.
doi: 10.1007/s00033-013-0345-x. |
[5] |
C. Dou, S. Jiang and Y. Ou,
Low Mach number limit of full Navier-Stokes equations in a 3D bounded domain, J. Differential Equations, 258 (2015), 379-398.
doi: 10.1016/j.jde.2014.09.017. |
[6] |
C. Dou, S. Jiang and Q. Ju,
Global existence and the low Mach number limit for the compressible magnetohydrodynamic equations in a bounded domain with perfectly conducting boundary, Z. Angew. Math. Phys., 64 (2013), 1661-1678.
doi: 10.1007/s00033-013-0311-7. |
[7] |
I. Dravić, N. Mujaković, 3-D flow of a compressible viscous micropolar fluid with spherical symmetry: a local existence theorem, Bound. Value Probl. , 2012 (2012), 25pp.
doi: 10.1186/1687-2770-2012-69. |
[8] |
I. Dra$\mathbf{v}$ić and N. Mujaković,
3-D flow of a compressible viscous micropolar fluid with spherical symmetry: Large time behavior of the solution, J. Math. Anal. Appl., 431 (2015), 545-568.
doi: 10.1016/j.jmaa.2015.06.002. |
[9] |
A. C. Eringen,
Theory of micropolar fluids, J. Math. Mech., 16 (1966), 1-18.
|
[10] |
J. Fan, H. Gao and B. Guo,
Low Mach number limit of the compressible magnetohydrodynamic equations with zero thermal conductivity coefficient, Math. Methods Appl. Sci., 34 (2011), 2181-2188.
doi: 10.1002/mma.1515. |
[11] |
J. Fan, F. Li and G. Nakamura,
Uniform well-posedness and singular limits of the isentropic Navier-Stokes-Maxwell system in a bounded domain, Z. Angew. Math. Phys., 66 (2015), 1581-1593.
doi: 10.1007/s00033-014-0484-8. |
[12] |
J. Fan, F. Li and G. Nakamura, Global existence and low Mach number limit to the 3D compressible magnetohydrodynamic equations in a bounded domain, Dynamical Systems, Differential equations and Applications, Proc. of 10th AIMS Conference, (2015), 387–394.
doi: 10.3934/proc.2015.0387. |
[13] |
E. Feireisl and A. Novotný,
The low Mach number limit for the full Navier-Stokes-Fourier system, Arch. Ration. Mech. Anal., 186 (2007), 77-107.
doi: 10.1007/s00205-007-0066-4. |
[14] |
I. Fërste,
On the theory of micropolar fluids, Adv. in Mech., 2 (1979), 81-100.
|
[15] |
P. Galdi and S. Rionero,
A note on the existence and uniqueness of the micropolar fluid equations, Int. J. Eng. Sci., 15 (1977), 105-108.
doi: 10.1016/0020-7225(77)90025-8. |
[16] |
X. Hu and D. Wang,
Low Mach number limit of viscous compressible magnetohydrodynamic flows, SIAM J. Math. Anal., 41 (2009), 1272-1294.
doi: 10.1137/080723983. |
[17] |
S. Jiang, Q. Ju and F. Li,
Low Mach limits for the multi-dimensional full Magnetohydrodynamic equations, Nonlinearity, 25 (2012), 1351-1365.
doi: 10.1088/0951-7715/25/5/1351. |
[18] |
S. Jiang, Q. Ju, F. Li and Z. Xin,
Low Mach numberlimit for the full compressible magnetohydrodynamic equations with general initial data, Adv. Math., 259 (2014), 384-420.
doi: 10.1016/j.aim.2014.03.022. |
[19] |
H. Lange,
The existence of instationary flows of incompressible micropolar fluids, Arch. Mech., 29 (1977), 741-744.
|
[20] |
F. Li and Y. Mu,
Low Mach limits of the full compressible Navier-Stokes-Maxwell system, J. Math. Anal. Appl., 412 (2014), 334-344.
doi: 10.1016/j.jmaa.2013.10.064. |
[21] |
P. L. Lions,
Mathematical Topics in Fluid Mechanics, Vol. 2 Compressible Models, Oxford University Press, New York, 1998. |
[22] |
G. Łukaszewicz,
Long time behavior of 2D micropolar fluid flows, Math. Comput. Model., 34 (2001), 487-509.
doi: 10.1016/S0895-7177(01)00078-4. |
[23] |
G. Łukaszewicz,
Asymptotic behavior of micropolar fluid flows, Int. J. Eng. Sci., 41 (2003), 259-269.
doi: 10.1016/S0020-7225(02)00208-2. |
[24] |
G. Łukaszewicz,
Micropolar Fluids. Theory and Applications, Birkhäuser, Boston, 1999.
doi: 10.1007/978-1-4612-0641-5. |
[25] |
G. Lukaszewicz, M. Rojas-Medar and M. Santos,
Stationary micropolar fluid with boundary data in $L^2$, J. Math. Anal. Appl., 271 (2002), 91-107.
doi: 10.1016/S0022-247X(02)00100-2. |
[26] |
M. A. Rojas-Medar,
Magneto-Micropolar fluid motion: Existence and uniqueness of strong solution, Math. Nachr., 188 (1997), 301-319.
doi: 10.1002/mana.19971880116. |
[27] |
F. V. Silva,
Leray's problem for a viscous incompressible micropolar fluid, J. Math. Anal. Appl., 306 (2005), 692-713.
doi: 10.1016/j.jmaa.2004.10.007. |
[28] |
J. Su,
Incompressible limit of a compressible micropolar fluid model with general initial data, Nonlinear Anal., 132 (2016), 1-24.
doi: 10.1016/j.na.2015.10.020. |
[29] |
J. Su, Low Mach number limit of a compressible micropolar fluid model,
(submitted). |
[30] |
X. Yang,
Low Mach number limit of the compressible Hall-magnetohydrodynamic system, Nonlinear Anal. Real World Appl., 25 (2015), 118-126.
doi: 10.1016/j.nonrwa.2015.03.007. |
[1] |
Jishan Fan, Fucai Li, Gen Nakamura. Global existence and low Mach number limit to the 3D compressible magnetohydrodynamic equations in a bounded domain. Conference Publications, 2015, 2015 (special) : 387-394. doi: 10.3934/proc.2015.0387 |
[2] |
Fucai Li, Yanmin Mu. Low Mach number limit for the compressible magnetohydrodynamic equations in a periodic domain. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 1669-1705. doi: 10.3934/dcds.2018069 |
[3] |
Donatella Donatelli, Bernard Ducomet, Šárka Nečasová. Low Mach number limit for a model of accretion disk. Discrete and Continuous Dynamical Systems, 2018, 38 (7) : 3239-3268. doi: 10.3934/dcds.2018141 |
[4] |
Yi-Long Luo, Yangjun Ma. Low Mach number limit for the compressible inertial Qian-Sheng model of liquid crystals: Convergence for classical solutions. Discrete and Continuous Dynamical Systems, 2021, 41 (2) : 921-966. doi: 10.3934/dcds.2020304 |
[5] |
Jishan Fan, Fucai Li, Gen Nakamura. Low Mach number limit of the full compressible Hall-MHD system. Communications on Pure and Applied Analysis, 2017, 16 (5) : 1731-1740. doi: 10.3934/cpaa.2017084 |
[6] |
Thomas Alazard. A minicourse on the low Mach number limit. Discrete and Continuous Dynamical Systems - S, 2008, 1 (3) : 365-404. doi: 10.3934/dcdss.2008.1.365 |
[7] |
Fucai Li, Yanmin Mu, Dehua Wang. Local well-posedness and low Mach number limit of the compressible magnetohydrodynamic equations in critical spaces. Kinetic and Related Models, 2017, 10 (3) : 741-784. doi: 10.3934/krm.2017030 |
[8] |
Lan Zeng, Guoxi Ni, Yingying Li. Low Mach number limit of strong solutions for 3-D full compressible MHD equations with Dirichlet boundary condition. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5503-5522. doi: 10.3934/dcdsb.2019068 |
[9] |
Eduard Feireisl, Hana Petzeltová. Low Mach number asymptotics for reacting compressible fluid flows. Discrete and Continuous Dynamical Systems, 2010, 26 (2) : 455-480. doi: 10.3934/dcds.2010.26.455 |
[10] |
Konstantina Trivisa. Global existence and asymptotic analysis of solutions to a model for the dynamic combustion of compressible fluids. Conference Publications, 2003, 2003 (Special) : 852-863. doi: 10.3934/proc.2003.2003.852 |
[11] |
Zefu Feng, Changjiang Zhu. Global classical large solution to compressible viscous micropolar and heat-conducting fluids with vacuum. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3069-3097. doi: 10.3934/dcds.2019127 |
[12] |
Zaynab Salloum. Flows of weakly compressible viscoelastic fluids through a regular bounded domain with inflow-outflow boundary conditions. Communications on Pure and Applied Analysis, 2010, 9 (3) : 625-642. doi: 10.3934/cpaa.2010.9.625 |
[13] |
Paolo Secchi. An alpha model for compressible fluids. Discrete and Continuous Dynamical Systems - S, 2010, 3 (2) : 351-359. doi: 10.3934/dcdss.2010.3.351 |
[14] |
Lvqiao liu, Lan Zhang. Optimal decay to the non-isentropic compressible micropolar fluids. Communications on Pure and Applied Analysis, 2020, 19 (9) : 4575-4598. doi: 10.3934/cpaa.2020207 |
[15] |
Stefano Scrobogna. Global existence and convergence of nondimensionalized incompressible Navier-Stokes equations in low Froude number regime. Discrete and Continuous Dynamical Systems, 2020, 40 (9) : 5471-5511. doi: 10.3934/dcds.2020235 |
[16] |
Weike Wang, Yucheng Wang. Global existence and large time behavior for the chemotaxis–shallow water system in a bounded domain. Discrete and Continuous Dynamical Systems, 2020, 40 (11) : 6379-6409. doi: 10.3934/dcds.2020284 |
[17] |
Lan Huang, Zhiying Sun, Xin-Guang Yang, Alain Miranville. Global behavior for the classical solution of compressible viscous micropolar fluid with cylinder symmetry. Communications on Pure and Applied Analysis, 2022, 21 (5) : 1595-1620. doi: 10.3934/cpaa.2022033 |
[18] |
Manuel Núñez. Existence of solutions of the equations of electron magnetohydrodynamics in a bounded domain. Discrete and Continuous Dynamical Systems, 2010, 26 (3) : 1019-1034. doi: 10.3934/dcds.2010.26.1019 |
[19] |
Guochun Wu, Yinghui Zhang. Global analysis of strong solutions for the viscous liquid-gas two-phase flow model in a bounded domain. Discrete and Continuous Dynamical Systems - B, 2018, 23 (4) : 1411-1429. doi: 10.3934/dcdsb.2018157 |
[20] |
Fucai Li, Yue Li. Global weak solutions for a kinetic-fluid model with local alignment force in a bounded domain. Communications on Pure and Applied Analysis, 2021, 20 (10) : 3583-3604. doi: 10.3934/cpaa.2021122 |
2020 Impact Factor: 1.392
Tools
Metrics
Other articles
by authors
[Back to Top]