Previous |  Up |  Next

Article

Title: Local-in-time existence for the non-resistive incompressible magneto-micropolar fluids (English)
Author: Zhang, Peixin
Author: Zhu, Mingxuan
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 67
Issue: 2
Year: 2022
Pages: 199-208
Summary lang: English
.
Category: math
.
Summary: We establish the local-in-time existence of a solution to the non-resistive magneto-micropolar fluids with the initial data $u_0\in H^{s-1+\varepsilon }$, $w_0\in H^{s-1}$ and $b_0\in H^{s}$ for $s>\frac {3}{2}$ and any $0<\varepsilon <1$. The initial regularity of the micro-rotational velocity $w$ is weaker than velocity of the fluid $u$. (English)
Keyword: non-resistive magneto-micropolar fluid
Keyword: local existence
MSC: 35A01
MSC: 35Q30
MSC: 76B03
MSC: 76W05
idZBL: Zbl 07511501
idMR: MR4396684
DOI: 10.21136/AM.2021.0111-20
.
Date available: 2022-03-25T08:22:40Z
Last updated: 2024-05-06
Stable URL: http://hdl.handle.net/10338.dmlcz/149566
.
Reference: [1] Ahmadi, G., Shahinpoor, M.: Universal stability of magneto-micropolar fluid motions.Int. J. Engin. Sci. 12 (1974), 657-663. Zbl 0284.76009, MR 0443550, 10.1016/0020-7225(74)90042-1
Reference: [2] Blömker, D., Nolde, C., Robinson, J. C.: Rigorous numerical verification of uniqueness and smoothness in a surface growth model.J. Math. Anal. Appl. 429 (2015), 311-325. Zbl 1315.65092, MR 3339076, 10.1016/j.jmaa.2015.04.025
Reference: [3] Chemin, J.-Y., McCormick, D. S., Robinson, J. C., Rodrigo, J. L.: Local existence for the non-resistive MHD equations in Besov spaces.Adv. Math. 286 (2016), 1-31. Zbl 1333.35183, MR 3415680, 10.1016/j.aim.2015.09.004
Reference: [4] Chen, M.: 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. Zbl 1299.35043, MR 3072129, 10.1016/S0252-9602(13)60051-X
Reference: [5] 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. 65 (2014), 687-710. Zbl 1300.35091, MR 3238510, 10.1007/s00033-013-0345-x
Reference: [6] Cowin, S. C.: Polar fluids.Phys. Fluids 11 (1968), 1919-1927. Zbl 0179.56002, 10.1063/1.1692219
Reference: [7] Erdoğan, M. E.: Polar effects in the apparent viscosity of suspension.Rheol. Acta 9 (1970), 434-438. 10.1007/BF01975413
Reference: [8] Fefferman, C. L., McCormick, D. S., Robinson, J. C., Rodrigo, J. L.: Higher order commutator estimates and local existence for the non-resistive MHD equations and related models.J. Funct. Anal. 267 (2014), 1035-1056. Zbl 1296.35142, MR 3217057, 10.1016/j.jfa.2014.03.021
Reference: [9] Fefferman, C. L., McCormick, D. S., Robinson, J. C., Rodrigo, J. L.: Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces.Arch. Ration. Mech. Anal. 223 (2017), 677-691. Zbl 1359.35150, MR 3590662, 10.1007/s00205-016-1042-7
Reference: [10] Jiu, Q., Niu, D.: Mathematical results related to a two-dimensional magneto-hydrody-namic equations.Acta Math. Sci., Ser. B, Engl. Ed. 26 (2006), 744-756. Zbl 1188.35148, MR 2265204, 10.1016/S0252-9602(06)60101-X
Reference: [11] Kato, T., Ponce, G.: Commutator estimates and the Euler and Navier-Stokes equations.Commun. Pure Appl. Math. 41 (1988), 891-907. Zbl 0671.35066, MR 0951744, 10.1002/cpa.3160410704
Reference: [12] Kenig, C. E., Ponce, G., Vega, L.: Well-posedness of the initial value problem for the Korteweg-de Vries equation.J. Am. Math. Soc. 4 (1991), 323-347. Zbl 0737.35102, MR 1086966, 10.1090/S0894-0347-1991-1086966-0
Reference: [13] {Ł}ukaszewicz, G.: Micropolar Fluids: Theory and Applications.Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston (1999). Zbl 0923.76003, MR 1711268, 10.1007/978-1-4612-0641-5
Reference: [14] Ortega-Torres, E. E., Rojas-Medar, M. A.: Magneto-micropolar fluid motion: Global existence of strong solutions.Abstr. Appl. Anal. 4 (1999), 109-125. Zbl 0976.35055, MR 1810322, 10.1155/S1085337599000287
Reference: [15] Rojas-Medar, M. A.: Magneto-micropolar fluid motion: Existence and uniqueness of strong solution.Math. Nachr. 188 (1997), 301-319. Zbl 0893.76006, MR 1484679, 10.1002/mana.19971880116
Reference: [16] Rojas-Medar, M. A.: Magneto-micropolar fluid motion: On the convergence rate of the spectral Galerkin approximations.Z. Angew. Math. Mech. 77 (1997), 723-732. Zbl 0894.76093, MR 1479160, 10.1002/zamm.19970771003
Reference: [17] Rojas-Medar, M. A., Boldrini, J. L.: Magneto-micropolar fluid motion: Existence of weak solutions.Rev. Mat. Complut. 11 (1998), 443-460. Zbl 0918.35114, MR 1666509, 10.5209/rev_REMA.1998.v11.n2.17276
Reference: [18] Yuan, J.: Existence theorem and blow-up criterion of strong solutions to the magneto-micropolar fluid equations.Math. Methods Appl. Sci. 31 (2008), 1113-1130. Zbl 1137.76071, MR 2419091, 10.1002/mma.967
Reference: [19] Yuan, B., Li, X.: Regularity of weak solutions to the 3D magneto-micropolar equations in Besov spaces.Acta Appl. Math. 163 (2019), 207-223. Zbl 1428.35409, MR 4008703, 10.1007/s10440-018-0220-z
Reference: [20] Zhang, Z.: A regularity criterion for the three-dimensional micropolar fluid system in homogeneous Besov spaces.Electron. J. Qual. Theory Differ. Equ. 2016 (2016), Article ID 104, 6 pages. Zbl 1399.35307, MR 3578430, 10.14232/ejqtde.2016.1.104
.

Files

Files Size Format View
AplMat_67-2022-2_5.pdf 216.7Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo