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.
Citation: |
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.![]() ![]() ![]() |
|
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.![]() ![]() ![]() |
|
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.![]() ![]() ![]() |
|
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.![]() ![]() ![]() |
|
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.![]() ![]() ![]() |
|
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.![]() ![]() ![]() |
|
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.![]() ![]() ![]() |
|
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.![]() ![]() ![]() |
|
A. C. Eringen
, Theory of micropolar fluids, J. Math. Mech., 16 (1966)
, 1-18.
![]() ![]() |
|
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.![]() ![]() ![]() |
|
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.![]() ![]() ![]() |
|
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.![]() ![]() ![]() |
|
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.![]() ![]() ![]() |
|
I. Fërste
, On the theory of micropolar fluids, Adv. in Mech., 2 (1979)
, 81-100.
![]() ![]() |
|
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.![]() ![]() ![]() |
|
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.![]() ![]() ![]() |
|
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.![]() ![]() ![]() |
|
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.![]() ![]() |
|
H. Lange
, The existence of instationary flows of incompressible micropolar fluids, Arch. Mech., 29 (1977)
, 741-744.
![]() ![]() |
|
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.![]() ![]() ![]() |
|
P. L. Lions,
Mathematical Topics in Fluid Mechanics, Vol. 2 Compressible Models, Oxford University Press, New York, 1998.
![]() ![]() |
|
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.![]() ![]() ![]() |
|
G. Łukaszewicz
, Asymptotic behavior of micropolar fluid flows, Int. J. Eng. Sci., 41 (2003)
, 259-269.
doi: 10.1016/S0020-7225(02)00208-2.![]() ![]() ![]() |
|
G. Łukaszewicz,
Micropolar Fluids. Theory and Applications, Birkhäuser, Boston, 1999.
doi: 10.1007/978-1-4612-0641-5.![]() ![]() ![]() |
|
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.![]() ![]() ![]() |
|
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.![]() ![]() ![]() |
|
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.![]() ![]() ![]() |
|
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.![]() ![]() ![]() |
|
J. Su, Low Mach number limit of a compressible micropolar fluid model,
(submitted).
![]() |
|
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.![]() ![]() ![]() |