Regularity criterion of three dimensional magneto-micropolar fluid equations with fractional dissipation

Yazhou Wang; Yuzhu Wang; Yazhou Wang; Yuzhu Wang

doi:10.3934/era.2024199

Electronic Research Archive

2024, Volume 32, Issue 7: 4416-4432. doi: 10.3934/era.2024199

Previous Article Next Article

Research article

Regularity criterion of three dimensional magneto-micropolar fluid equations with fractional dissipation

Yazhou Wang ,
Yuzhu Wang ^,

School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450011, China

Received: 16 March 2024 Revised: 24 May 2024 Accepted: 27 June 2024 Published: 11 July 2024

In this paper, we investigate the regularity criterion of weak solutions to three-dimensional magneto-micropolar fluid equations with fractional dissipation. A regularity criterion is established via the third component of the velocity fields, the micro-rotational velocity fields, and the magnetic fields.
- magneto-micropolar fluid equations,
- fractional dissipation,
- regularity criterion,
- weak solutions
Citation: Yazhou Wang, Yuzhu Wang. Regularity criterion of three dimensional magneto-micropolar fluid equations with fractional dissipation[J]. Electronic Research Archive, 2024, 32(7): 4416-4432. doi: 10.3934/era.2024199

Related Papers:

Abstract

In this paper, we investigate the regularity criterion of weak solutions to three-dimensional magneto-micropolar fluid equations with fractional dissipation. A regularity criterion is established via the third component of the velocity fields, the micro-rotational velocity fields, and the magnetic fields.

References

[1]	J. Fan, X. Zhong, Regularity criteria for 3D generalized incompressible magneto-micropolar fluid equations, Appl. Math. Lett., 127 (2022), 107840. https://doi.org/10.1016/j.aml.2021.107840 doi: 10.1016/j.aml.2021.107840
[2]	H. Qiu, C. Xiao, Z. Yao, Local existence for the d-dimensional magneto-micropolar equations with fractional dissipation in Besov spaces, Math. Methods Appl. Sci., 46 (2023), 9617–9651. https://doi.org/10.1002/mma.9078 doi: 10.1002/mma.9078
[3]	B. Yuan, P. Zhang, Global well-posedness for the 3D magneto-micropolar equations with fractional dissipation, N. Z. J. Math., 51 (2021), 119–130. https://doi.org/10.53733/161 doi: 10.53733/161
[4]	J. Yan, Q. Xie, B. Dong, Global regularity of the 3D magneto-micropolar equations with fractional dissipation, Z. Angew. Math. Phys., 73 (2022), 1–15. https://doi.org/10.1007/s00033-021-01651-2 doi: 10.1007/s00033-021-01651-2
[5]	E. Ortega-Torres, M.Rojas-Medar, Magneto-micropolar fluid motion: global existence of strong solutions, Abstr. Appl. Anal., 4 (1999), 109–125. https://doi.org/10.1155/S1085337599000287 doi: 10.1155/S1085337599000287
[6]	M. Rojas-Medar, Magneto-micropolar fluid motion: existence and uniqueness of strong solutions, Math. Nachr., 188 (1997), 307–319. https://doi.org/10.1002/mana.19971880116 doi: 10.1002/mana.19971880116
[7]	M. Rojas-Medar, J. Boldrini, Magneto-micropolar fluid motion: existence of weak solutions, Rev. Mat. Complutense, 11 (1998), 443–460.
[8]	S. Gala, Regularity criteria for the 3D magneto-micropolar fluid equations in the Morrey-Campanato space, Nonlinear Differ. Equations Appl., 17 (2010), 181–194. https://doi.org/10.1007/s00030-009-0047-4 doi: 10.1007/s00030-009-0047-4
[9]	Z. Li, P. Niu, New regularity criteria for the 3D magneto-micropolar fluid equations in Lorentz spaces, Math. Methods Appl. Sci., 44 (2021), 6056–6066. https://doi.org/10.1002/mma.7170 doi: 10.1002/mma.7170
[10]	F. Xu, Regularity criterion of weak solution for the 3D magneto-micropolar fluid equations in Besov spaces, Commun. Nonlinear. Sci. Numer. Simul., 17 (2012), 2426–2433. http://doi.org/10.1016/j.cnsns.2011.09.038 doi: 10.1016/j.cnsns.2011.09.038
[11]	Z. Zhang, Z. Yao, X. Wang, A regularity criterion for the 3D magneto-micropolar fluid equations in Triebel-Lizorkin spaces, Nonlinear Anal. Theory Methods Appl., 74 (2011), 2220–2225. https://doi.org/10.1016/J.NA.2010.11.026 doi: 10.1016/J.NA.2010.11.026
[12]	F. Xu, X. Xu, J. Yuan, Logarithmically improved regularity criteria for the micropolar fluid equations, Appl. Math., 39 (2012), 315–328. https://doi.org/10.4064/am39-3-6 doi: 10.4064/am39-3-6
[13]	B. Yuan, Regularity of weak solutions to magneto-micropolar fluid equations, Acta Math. Sci., 30 (2010), 1469–1480. https://doi.org/10.1016/S0252-9602(10)60139-7 doi: 10.1016/S0252-9602(10)60139-7
[14]	S. Yan, X. Chen, Regularity criterion for the 3D magneto-micropolar fluid flows in terms of pressure, J. Nonlinear Evol. Equations Appl., 2022 (2023), 127–142.
[15]	Z. Zhang, Regularity criteria for the 3D magneto-micropolar fluid equations via the direction of the velocity, Proc. Math. Sci., 125 (2015), 37–43. https://doi.org/10.1007/s12044-015-0213-z doi: 10.1007/s12044-015-0213-z
[16]	Y. Z. Wang, Y. Wang, Blow-up criterion for two-dimensional magneto-micropolar fluid equations with partial viscosity, Math. Methods Appl. Sci., 34 (2011), 2125–2135. https://doi.org/10.1002/mma.1510 doi: 10.1002/mma.1510
[17]	J. Yuan, Existence theorem and blow-up criterion of the strong solutions to the magneto-micropolar fluid equations, Math. Methods Appl. Sci., 31 (2008), 1113–1130. https://doi.org/10.1002/mma.967 doi: 10.1002/mma.967
[18]	L. Deng, H. Shang, Global well-posedness for $n$-dimensional magneto-micropolar equations with hyperdissipation, Appl. Math. Lett., 111 (2021), 106610. https://doi.org/10.1016/j.aml.2020.106610 doi: 10.1016/j.aml.2020.106610
[19]	J. Liu, S. Wang, Initial-boundary value problem for 2D micropolar equations without angular viscosity, Commun. Math. Sci., 16 (2018), 2147–2165. https://doi.org/10.4310/CMS.2018.v16.n8.a5 doi: 10.4310/CMS.2018.v16.n8.a5
[20]	S. Wang, W. Xu, J. Liu, Initial-boundary value problem for 2D magneto-micropolar equations with zero angular viscosity, Z. Angew. Math. Phys., 72 (2021), 1–23. https://doi.org/10.1007/s00033-021-01537-3 doi: 10.1007/s00033-021-01537-3
[21]	H. Lin, S. Liu, H. Zhang, R. Bai, Global regularity of 2D incompressible magneto-micropolar fluid equations with partial viscosity, Acta Math. Sci., 43 (2023), 1275–1300. https://doi.org/10.1007/s10473-023-0316-z doi: 10.1007/s10473-023-0316-z
[22]	D. Regmi, J. Wu, Global regularity for the 2D magneto-micropolar equations with partial dissipation, J. Math. Study, 49 (2016), 169–194. https://doi.org/10.4208/jms.v49n2.16.05 doi: 10.4208/jms.v49n2.16.05
[23]	H. Shang, J. Zhao, Global regularity for 2D magneto-micropolar equations with only micro-rotational velocity dissipation and magnetic diffusion, Nonlinear Anal. Theory Methods Appl., 150 (2017), 194–209. https://doi.org/10.1016/j.na.2016.11.011 doi: 10.1016/j.na.2016.11.011
[24]	H. Shang, C. Gu, Global regularity and decay estimates for 2D magneto-micropolar equations with partial dissipation, Z. Angew. Math. Phys., 70 (2019), 1–22. https://doi.org/10.1007/s00033-019-1129-8 doi: 10.1007/s00033-019-1129-8
[25]	H. Shang, J. Wu, Global regularity for 2D fractional magneto-micropolar equations, Math. Z., 297 (2021), 775–802. https://doi.org/10.1007/s00209-020-02532-6 doi: 10.1007/s00209-020-02532-6
[26]	Y. Jia, Q. Xie, B. Dong, Global regularity of the 3D magneto-micropolar equations with fractional dissipation, Z. Angew. Math. Phys., 73 (2022), 1–15. https://doi.org/10.1007/s00033-021-01651-2 doi: 10.1007/s00033-021-01651-2
[27]	Y. Wang, L. Gu, Global regularity of 3D magneto-micropolar fluid equations, Appl. Math. Lett., 99 (2020), 105980. https://doi.org/10.1016/j.aml.2019.07.011 doi: 10.1016/j.aml.2019.07.011
[28]	J. Wu, Regularity criteria for the generalized MHD equations, Commun. Partial Differ. Equations, 33 (2008), 285–306. http://doi.org/10.1080/03605300701382530 doi: 10.1080/03605300701382530
[29]	J. Wu, Global regularity for a class of generalized magnetohydrodynamic equations, J. Math. Fluid Mech., 13 (2011), 295–305. https://doi.org/10.1007/s00021-009-0017-y doi: 10.1007/s00021-009-0017-y
[30]	Y. Zhou, Regularity criteria for the generalized viscous MHD equations, Ann. I. H. Poincaré C Anal. Non. Linéaire, 24 (2007), 491–505. https://doi.org/10.1016/j.anihpc.2006.03.014 doi: 10.1016/j.anihpc.2006.03.014
[31]	J. Wang, W. Tan, Y. Nie, A regularity criterion for the 3D generalized MHD system involving partial components, J. Math. Phys., 64 (2023), 051505. https://doi.org/10.1063/5.0143742 doi: 10.1063/5.0143742
[32]	Y. Cai, Z. Lei, Global well-posedness of the incompressible Magnetohydrodynamics, Arch. Ration. Mech. Anal., 228 (2018), 969–993. https://doi.org/10.1007/s00205-017-1210-4 doi: 10.1007/s00205-017-1210-4
[33]	B. Yuan, J. Zhao, Global regularity of 2D almost resistive MHD equations, Nonlinear Anal. Real World Appl., 41 (2018), 53–65. https://doi.org/10.1016/j.nonrwa.2017.10.006 doi: 10.1016/j.nonrwa.2017.10.006
[34]	Z. Lei, On axially symmetric incompressible Magnetohydrodynamics in three dimensions, J. Differ. Equations, 259 (2015), 3202–3215. https://doi.org/10.1016/j.jde.2015.04.017 doi: 10.1016/j.jde.2015.04.017
[35]	J. Serrin, On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Ration. Mech. Anal., 9 (1962), 187–195. https://doi.org/10.1007/BF00253344 doi: 10.1007/BF00253344
[36]	Y. Zhou, A new regularity criterion for weak solutions to the Navier-Stokes equations, J. Math. Pures Appl., 84 (2005), 1496–1514. http://doi.org/10.1016/j.matpur.2005.07.003 doi: 10.1016/j.matpur.2005.07.003
[37]	C. Cao, Sufficient conditions for the regularity to the 3D Navier-Stokes equations, Discrete Contin. Dyn. Syst., 26 (2010), 1141–1151. https://doi.org/10.3934/dcds.2010.26.1141 doi: 10.3934/dcds.2010.26.1141

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)