Uniform regularity for the isentropic compressible magneto-micropolar system
Abstract
In this paper, we are concerned with the uniform regularity estimates of smooth solutions to the isentropic compressible magneto-micropolar system in 
. Under the assumption that 
, and by applying the classic bilinear commutator and product estimates, the uniform estimates of solutions to the isentropic compressible magneto-micropolar system are established in 
space, 
.
Keyword : compressible, magneto-micropolar, uniform regularity
How to Cite
Fan, J., Wang, P., & Zhou, Y. (2021). Uniform regularity for the isentropic compressible magneto-micropolar system. Mathematical Modelling and Analysis, 26(4), 519-527. https://doi.org/10.3846/mma.2021.13632
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
T. Alazard. Low Mach number limit of the full Navier-Stokes equations. Archive for Rational Mechanics and Analysis, 180(1):1–73, 2006. https://doi.org/10.1007/s00205-005-0393-2
C. Dou, S. Jiang and Y. Ou. Low Mach number limit of full Navier-Stokes equations in a 3D bounded domain. Journal of Differential Equations, 258(2):379– 398, 2015. https://doi.org/10.1016/j.jde.2014.09.017
J. Fan and Y. Zhou. Local well-posedness for the isentropic compressible MHD system with vacuum. Journal of Mathematical Physics, 62(5):051505, 2021. https://doi.org/10.1063/5.0029046
H. Gong, J. Li, X.-G. Liu and X. Zhang. Local well-posedness of isentropic compressible Navier-Stokes equations with vacuum. Communications in Mathematical Sciences, 18(7):1891–1909, 2020. https://doi.org/10.4310/CMS.2020.v18.n7.a4
X. Huang. On local strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with vacuum. Science China Mathematics, 2020. https://doi.org/10.1007/s11425-019-9755-3
T. Kato and G. Ponce. Commutator estimates and the Euler and NavierStokes equations. Communications Pure and Applied Mathematics, 41(7):891– 907, 1988. https://doi.org/10.1002/cpa.3160410704
G. Métivier and S. Schochet. The incompressible limit of the non-isentropic Euler equations. Archive for Rational Mechanics and Analysis, 158(1):61–90, 2001. https://doi.org/10.1007/PL00004241
H. Triebel. Theory of function spaces, volume 78 of Monographs in Mathematics. Birkhäuser Verlag, Springer, Basel, 1983. https://doi.org/10.1007/978-3-0346-0416-1
G. Łukaszewicz. Micropolar Fluids. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston, Inc., Boston, MA, 1999. https://doi.org/10.1007/978-1-4612-0641-5_5
R. Wei, B. Guo and Y. Li. Global existence and optimal convergence rates of solutions for 3D compressible magneto-micropolar fluid equations. Journal of Differential Equations, 263(5):2457–2480, 2017. https://doi.org/10.1016/j.jde.2017.04.002
Z. Wu and W. Wang. The pointwise estimates of diffusion wave of the compressible micropolar fluids. Journal of Differential Equations, 265(6):2544–2576, 2018. https://doi.org/10.1016/j.jde.2018.04.039
X. Xu and J. Zhang. A blow-up criterion for 3D compressible magnetohydrodynamic equations with vacuum. Mathematical Models and Methods in Applied Sciences, 22(2):1150010, 2012. https://doi.org/10.1142/S0218202511500102
P. Zhang. Blow-up criterion for 3D compressible viscous magneto-micropolar fluids with initial vacuum. Boundary Value Problems, 2013(160):1–16, 2013. https://doi.org/10.1186/1687-2770-2013-160
L. Zhu and Y. Chen. A new blowup criterion for strong solutions to the Cauchy problem of three-dimensional compressible magnetohydrodynamic equations. Nonlinear Analysis: Real World Applications, 41:461–474, 2018. https://doi.org/10.1016/j.nonrwa.2017.10.018
C. Dou, S. Jiang and Y. Ou. Low Mach number limit of full Navier-Stokes equations in a 3D bounded domain. Journal of Differential Equations, 258(2):379– 398, 2015. https://doi.org/10.1016/j.jde.2014.09.017
J. Fan and Y. Zhou. Local well-posedness for the isentropic compressible MHD system with vacuum. Journal of Mathematical Physics, 62(5):051505, 2021. https://doi.org/10.1063/5.0029046
H. Gong, J. Li, X.-G. Liu and X. Zhang. Local well-posedness of isentropic compressible Navier-Stokes equations with vacuum. Communications in Mathematical Sciences, 18(7):1891–1909, 2020. https://doi.org/10.4310/CMS.2020.v18.n7.a4
X. Huang. On local strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with vacuum. Science China Mathematics, 2020. https://doi.org/10.1007/s11425-019-9755-3
T. Kato and G. Ponce. Commutator estimates and the Euler and NavierStokes equations. Communications Pure and Applied Mathematics, 41(7):891– 907, 1988. https://doi.org/10.1002/cpa.3160410704
G. Métivier and S. Schochet. The incompressible limit of the non-isentropic Euler equations. Archive for Rational Mechanics and Analysis, 158(1):61–90, 2001. https://doi.org/10.1007/PL00004241
H. Triebel. Theory of function spaces, volume 78 of Monographs in Mathematics. Birkhäuser Verlag, Springer, Basel, 1983. https://doi.org/10.1007/978-3-0346-0416-1
G. Łukaszewicz. Micropolar Fluids. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston, Inc., Boston, MA, 1999. https://doi.org/10.1007/978-1-4612-0641-5_5
R. Wei, B. Guo and Y. Li. Global existence and optimal convergence rates of solutions for 3D compressible magneto-micropolar fluid equations. Journal of Differential Equations, 263(5):2457–2480, 2017. https://doi.org/10.1016/j.jde.2017.04.002
Z. Wu and W. Wang. The pointwise estimates of diffusion wave of the compressible micropolar fluids. Journal of Differential Equations, 265(6):2544–2576, 2018. https://doi.org/10.1016/j.jde.2018.04.039
X. Xu and J. Zhang. A blow-up criterion for 3D compressible magnetohydrodynamic equations with vacuum. Mathematical Models and Methods in Applied Sciences, 22(2):1150010, 2012. https://doi.org/10.1142/S0218202511500102
P. Zhang. Blow-up criterion for 3D compressible viscous magneto-micropolar fluids with initial vacuum. Boundary Value Problems, 2013(160):1–16, 2013. https://doi.org/10.1186/1687-2770-2013-160
L. Zhu and Y. Chen. A new blowup criterion for strong solutions to the Cauchy problem of three-dimensional compressible magnetohydrodynamic equations. Nonlinear Analysis: Real World Applications, 41:461–474, 2018. https://doi.org/10.1016/j.nonrwa.2017.10.018