| Title:
|
A regularity criterion of 3D magneto-micropolar equations with the pressure term (English) |
| Author:
|
Kim, Jae-Myoung |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0011-4642 |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
151 |
| Issue:
|
1 |
| Year:
|
2026 |
| Pages:
|
57-66 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This work focuses on the 3D incompressible magneto-micropolar (MMP) equations with the mixed pressure-velocity-magnetic field in view of Lorentz spaces. Also, we generalize some known results to MMP equations in view of Besov spaces. (English) |
| Keyword:
|
3D magneto-micropolar equation |
| Keyword:
|
regularity criterion |
| Keyword:
|
pressure function |
| Keyword:
|
Besov space |
| MSC:
|
35B65 |
| MSC:
|
35Q35 |
| MSC:
|
76D05 |
| DOI:
|
10.21136/MB.2025.0008-24 |
| . |
| Date available:
|
2026-02-19T13:55:14Z |
| Last updated:
|
2026-02-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153386 |
| . |
| 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] Veiga, H. Beirão da, Yang, J.: On mixed pressure-velocity regularity criteria to the Navier-Stokes equations in Lorentz spaces.Chin. Ann. Math., Ser. B 42 (2021), 1-16. Zbl 1464.35169, MR 4209050, 10.1007/s11401-021-0242-0 |
| Reference:
|
[3] Bergh, J., Löfström, J.: Interpolation Spaces: An Introduction.Grundlehren der mathematischen Wissenschaften 223. Springer, Berlin (1976). Zbl 0344.46071, MR 0482275, 10.1007/978-3-642-66451-9 |
| Reference:
|
[4] Berselli, L. C., Galdi, G. P.: Regularity criteria involving the pressure for the weak solutions of the Navier-Stokes equations.Proc. Am. Math. Soc. 130 (2002), 3585-3595. Zbl 1075.35031, MR 1920038, 10.1090/S0002-9939-02-06697-2 |
| Reference:
|
[5] Dong, B.-Q., Jia, Y., Chen, Z.-M.: Pressure regularity criteria of the three-dimensional micropolar fluid flows.Math. Methods Appl. Sci. 34 (2011), 595-606. Zbl 1219.35189, MR 2814514, 10.1002/mma.1383 |
| Reference:
|
[6] Eringen, A. C.: Theory of micropolar fluids.J. Math. Mech. 16 (1967), 1-18. MR 0204005, 10.1512/iumj.1967.16.16001 |
| Reference:
|
[7] Gala, S.: A remark on the logarithmically improved regularity criterion for the micropolar fluid equations in terms of the pressure.Math. Methods Appl. Sci. 34 (2011), 1945-1953. Zbl 1230.35100, MR 2846510, 10.1002/mma.1488 |
| Reference:
|
[8] Gala, S., Ragusa, M. A.: Logarithmically improved regularity criterion for the Boussinesq equations in Besov spaces with negative indices.Appl. Anal. 95 (2016), 1271-1279. Zbl 1336.35289, MR 3479003, 10.1080/00036811.2015.1061122 |
| Reference:
|
[9] Gala, S., Ragusa, M. A., Zhang, Z.: A regularity criterion in terms of pressure for the 3D viscous MHD equations.Bull. Malays. Math. Sci. Soc. (2) 40 (2017), 1677-1690. Zbl 1386.35339, MR 3712578, 10.1007/s40840-015-0160-y |
| Reference:
|
[10] Giga, Y.: Solutions for semilinear parabolic equations in $L^p$ and regularity of weak solutions of the Navier-Stokes system.J. Differ. Equations 62 (1986), 186-212. Zbl 0577.35058, MR 0833416, 10.1016/0022-0396(86)90096-3 |
| Reference:
|
[11] Guo, Z., Kučera, P., Skalák, Z.: Regularity criterion for solutions to the Navier-Stokes equations in the whole 3D space based on two vorticity components.J. Math. Anal. Appl. 458 (2018), 755-766. Zbl 1378.35217, MR 3711930, 10.1016/j.jmaa.2017.09.029 |
| Reference:
|
[12] Ji, X., Wang, Y., Wei, W.: New regularity criteria based on pressure or gradient of velocity in Lorentz spaces for the 3D Navier-Stokes equations.J. Math. Fluid Mech. 22 (2020), Article ID 13, 8 pages. Zbl 1433.76033, MR 4067153, 10.1007/s00021-019-0476-8 |
| Reference:
|
[13] Kanamaru, R., Yamamoto, T.: Logarithmically improved extension criteria involving the pressure for the Navier-Stokes equations in $\Bbb R^n$.Math. Nachr. 296 (2023), 2859-2876. Zbl 1532.35346, MR 4626863, 10.1002/mana.202100281 |
| Reference:
|
[14] Kim, J.-M.: Regularity criteria of 3D generalized magneto-micropolar fluid system in terms of the pressure.Available at https://arxiv.org/abs/2310.00217 (2023), 13 pages. 10.48550/arXiv.2310.00217 |
| Reference:
|
[15] Kim, J.-M., Kim, J.: On mixed pressure-velocity regularity criteria for the 3D micropolar equations in Lorentz spaces.J. Chungcheong Math. Soc. 34 (2021), 85-92. MR 4229875, 10.14403/jcms.2021.34.1.85 |
| Reference:
|
[16] Li, Z., Niu, P.: New regularity criteria for the 3D magneto-micropolar fluid equations in Lorentz spaces.Math. Methods Appl. Sci. 44 (2021), 6056-6066. Zbl 1473.35448, MR 4251020, 10.1002/mma.7170 |
| Reference:
|
[17] Meyer, Y., Gérard, P., Oru, F.: Inégalités de Sobolev précisées.Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math., Palaiseau 4 (1996-1997), 8 pages French. Zbl 1066.46501, MR 1482810 |
| Reference:
|
[18] O'Neil, R.: Convolution operators and $L(p,q)$ spaces.Duke Math. J. 30 (1963), 129-142. Zbl 0178.47701, MR 0146673, 10.1215/S0012-7094-63-03015-1 |
| Reference:
|
[19] 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:
|
[20] Ragusa, M. A., Wu, F.: Eigenvalue regularity criteria of the three-dimensional micropolar fluid equations.Bull. Malays. Math. Sci. Soc. (2) 47 (2024), Article ID 76, 11 pages. Zbl 1541.35390, MR 4718588, 10.1007/s40840-024-01679-3 |
| Reference:
|
[21] 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:
|
[22] Sawano, Y.: Homogeneous Besov spaces.Kyoto J. Math. 60 (2020), 1-43. Zbl 1437.42034, MR 4065179, 10.1215/21562261-2019-0038 |
| Reference:
|
[23] Suzuki, T.: A remark on the regularity of weak solutions to the Navier-Stokes equations in terms of the pressure in Lorentz spaces.Nonlinear Anal., Theory Methods Appl., Ser. A 75 (2012), 3849-3853. Zbl 1239.35115, MR 2914575, 10.1016/j.na.2012.02.006 |
| Reference:
|
[24] Suzuki, T.: Regularity criteria of weak solutions in terms of the pressure in Lorentz spaces to the Navier-Stokes equations.J. Math. Fluid Mech. 14 (2012), 653-660. Zbl 1256.35066, MR 2992034, 10.1007/s00021-012-0098-x |
| Reference:
|
[25] Zhou, Y.: Regularity criteria for the 3D MHD equations in terms of the pressure.Int. J. Non-Linear Mech. 41 (2006), 1174-1180. Zbl 1160.35506, MR 2308660, 10.1016/j.ijnonlinmec.2006.12.001 |
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