Global low-energy weak solutions for compressible magneto-micropolar fluids with discontinuous initial data in R^3
DOI:
https://doi.org/10.58997/ejde.2023.86Keywords:
Magneto-micropolar fluids; weak solutions; global-in-time existence; low-energyAbstract
This article concerns the weak solutions of a 3D Cauchy problem of compressible magneto-micropolar fluids with discontinuous initial data. Under the assumption that the initial data are of small energy and the initial density is positive and essentially bounded, we establish the existence of weak solutions that are global-in-time. Moreover, we obtain the large-time behavior of such solutions.
For moreinformation see https://ejde.math.txstate.edu/Volumes/2023/86/abstr.html
References
R. A. Adams; Sobolev Space, Academic Press, New York, 1975.
G. Ahmadi, M. Shahinpoor; Universal stability of magneto-micropolar fluid motions, Internat. J. Engrg. Sci., 12 (1974), 657-663.
Y. Amirat, K. Hamdache; Weak solutions to the equations of motion for compressible magnetic fluids, J. Math. Pures Appl., 91 (2009), 433-467.
A. C. Eringen; Theory of micropolar fluids, J. Math. Mech., 16 (1966), 1-18.
E. Feireisl, H. PetzeltovŽa; Large-time behavior of solutions to the Navier-Stokes equations of compressible flow, Arch. Ration. Mech. Anal., 150 (1999), 77-96.
E. Feireisl, A. NovotnŽy, H. Petzeltov`a; On the existence of globally defined weak solutions to the Navier-Stokes equations, J. Math. Fluid Mech., 3 (2001), 358-392.
E. Feireisl; Dynamics of viscous compressible fluids, Oxford Lecture Series in Mathematics and its Applications, Oxford University Press, Oxford, 2004.
D. Hoff; Global solutions of the Navier-Stokes equations for multidimensional compressible flow with discontinuous initial data, J. Differential Equations, 120 (1995), 215-254.
D. Hoff; Strong convergence to global solutions for multidimensional flows of compressible, viscous fluids with polytropic equations of state and discontinuous initial data, Arch. Ration. Mech. Anal., 132 (1995), 1-14.
X. D. Huang, J. Li, Z. P. Xin; Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations, Commun. Pure Appl. Math., 65 (2012), 549-585.
X. P. Hu, D. H. Wang; Global existence and large-time behavior of solutions to the three dimensional equations of compressible magnetohydrodynamic flows, Arch. Ration. Mech. Anal., 197 (2010), 203-238.
Y. Kagei, S. Kawashima; Local solvability of an initial boundary value problem for a quasilinear hyperbolic-parabolic system, J. Hyper. Differ. Equ., 3 (2006), 195-232.
S. Kawashima; Systems of a hyperbolic-parabolic composite type, with applications to the equations of magnetohydrodynamics, Ph.D. Thesis, Kyoto University, 1983.
P. L. Lions; Mathematical Topics in Fluid Mechanics: Compressible Models, Oxford University Press, Oxford, 1998.
Q. Q. Liu, P. X. Zhang; Optimal time decay of the compressible micropolar fluids, J. Differential Equations, 260(10) (2016), 7634-7661.
S. Q. Liu, H. B. Yu, J. W. Zhang; Global weak solutions of 3D compressible MHD with discontinuous initial data and vacuum, J. Differential Equations, 254 (2013), 229-255.
G. Lukaszewicz; Micropolar Fluids: Theory and Applications Modeling and Simulation in Science, Engineering and Technology, Birkhšauser, Boston, 1999.
A. Matsumura, T. Nishida; The initial value problem for the equations of motion of compressible viscous and heat conductive fluids, Proc. Japan Acad. Ser. A, 55 (1979), 337-342.
A. Matsumura, T. Nishida; The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ., 20 (1980), 67-104.
N. MujakoviŽc; One-dimensional flow of a compressible viscous micropolar fluid: regularity of the solution, Rad. Mat., 10(2) (2001), 181-193.
N. MujakoviŽc; Global in time estimates for one-dimensional compressible viscous micropolar fluid model, Glas. Mat. Ser. III, 40(60) (2005), 103-120.
N. MujakoviŽc; Non-homogeneous boundary value problem for one-dimensional compressible viscous micropolar fluid model: a local existence theorem, Ann. Univ. Ferrara Sez. VII Sci. Mat., 53(2) (2007), 361-379.
L. N. Qin, Y. H. Zhang; Optimal decay rates for higher-order derivatives of solutions to the 3D compressible micropolar fluids system, J. Math. Anal. Appl., 512(1) (2022), 126116.
M. A. Rojas-Medar, J. L. Boldrini; Magneto-micropolar fluid motion: existence of weak solution, Rev. Math. Comp., 11 (1998), 443-460.
A. Suen; Existence and uniqueness of low-energy weak solutions to the compressible 3D magnetohydrodynamics equations, J. Differential Equations, 268 (2020), 2622-2671.
A. Suen, D. Hoff; Global low-energy weak solutions of the equations of three-dimensional compressible magnetohydrodynamics, Arch. Ration. Mech. Anal., 205 (2012), 27-58.
L. L. Tong, R. H. Pan, Z. Tan; Decay estimates of solutions to the compressible micropolar fluids system in R3, J. Differential Equations, 293 (2021), 520-552.
L. L. Tong, Z. Tan; Optimal decay rates of the compressible magneto-micropolar fluids system in R3, Commun. Math. Sci., 17 (2019), 1109-1134.
A. Valli; An existence theorem for compressible viscous fluids, Ann. Mat. Pura Appl., 130 (1982) 197-213.
R. Y. Wei, B. L. Guo, Y. Li; Global existence and optimal convergence rates of solutions for 3D compressible magneto-micropolar fluid equations, J. Differential Equations, 263 (2017) 2457-2480.
G. C. Wu, Y.H. Zhang, W. Y. Zou; Optimal time-decay rates for the 3D compressible magnetohydrodynamic flows with discontinuous initial data and large oscillations, J. Lond. Math. Soc., 103 (2021), 817-845.
Q. J. Xu, Z. Tan, H. Q, Wang, L. L. Tong; Global low-energy weak solutions of the compressible magneto-micropolar fluids in the half-space, Z. Angew. Math. Phys., 73 (2022), 223.
W. P. Ziemer; Weakly differentiable functions. Sobolev Spaces and Functions of Bounded Variation, Graduate Texts in Mathematics, vol. 120. Springer, New York, 1989.
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