Fan, Jishan; Li, Fucai; Nakamura, Gen Regularity criteria for the incompressible Hall-magnetohydrodynamic equations. (English) Zbl 1297.35067 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 109, 173-179 (2014). Summary: We establish some new regularity criteria for the three-dimensional incompressible Hall-magnetohydrodynamic equations. Cited in 30 Documents MSC: 35B65 Smoothness and regularity of solutions to PDEs 35Q35 PDEs in connection with fluid mechanics 76W05 Magnetohydrodynamics and electrohydrodynamics 70S15 Yang-Mills and other gauge theories in mechanics of particles and systems Keywords:Besov space PDF BibTeX XML Cite \textit{J. Fan} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 109, 173--179 (2014; Zbl 1297.35067) Full Text: DOI References: [1] Lighthill, M. J., Studies on magneto-hydrodynamic waves and other anisotropic wave motions, Philos. Trans. R. Soc. Lond. Ser. A, 252, 397-430, (1960) · Zbl 0097.20806 [2] Polygiannakis, J. M.; Moussas, X., A review of magneto-vorticity induction in Hall-MHD plasmas, Plasma Phys. Control. Fusion, 43, 195-221, (2001) [3] Fan, J.; Jiang, S.; Nakamura, G.; Zhou, Y., Logarithmically improved regularity criteria for the Navier-Stokes and MHD equations, J. Math. Fluid Mech., 13, 557-571, (2011) · Zbl 1270.35339 [4] Zhou, Y.; Fan, J., Logarithmically improved regularity criteria for the 3D viscous MHD equations, Forum Math., 24, 691-708, (2012) · Zbl 1247.35115 [5] Chen, Q.; Miao, C.; Zhang, Z., On the regularity criterion of weak solution for the 3D viscous magnetohydrodynamic equations, Comm. Math. Phys., 284, 919-930, (2008) · Zbl 1168.35035 [6] Lei, Z.; Zhou, Y., BKM’s criterion and global weak solutions for magnetohydrodynamics with zero viscosity, Discrete Contin. Dyn. Syst., 25, 2, 575-583, (2009) · Zbl 1171.35452 [7] Zhou, Y., Regularity criteria for the 3D MHD equations in terms of the pressure, Internat. J. Non-Linear Mech., 41, 1174-1180, (2006) · Zbl 1160.35506 [8] Acheritogaray, M.; Degond, P.; Frouvelle, A.; Liu, J.-G., Kinetic formulation and global existence for the Hall-magnetohydrodynamics system, Kinet. Relat. Models, 4, 901-918, (2011) · Zbl 1251.35076 [9] Chae, D.; Lee, J., On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics, J. Differential Equations, 256, 11, 3835-3858, (2014) · Zbl 1295.35122 [10] Chae, D.; Schonbek, M., On the temporal decay for the Hall-magnetohydrodynamic equations, J. Differential Equations, 255, 11, 3971-3982, (2013) · Zbl 1291.35212 [11] Chae, D.; Degond, P.; Liu, J.-G., Well-posedness for Hall-magnetohydrodynamics, Ann. Inst. H. Poincaré Anal. Non Linéaire, 31, 555-565, (2014) · Zbl 1297.35064 [12] D. Chae, S. Weng, Singularity formation for the incompressible Hall-MHD equations without resistivity, 19 December 2013, arXiv:1312.5519v1 [math. AP]. · Zbl 1347.35199 [13] Dumas, E.; Sueur, F., On the weak solutions to the Maxwell-Landau-Lifshitz equations and to the Hall-Magneto-Hydrodynamic equations, Comm. Math. Phys., 330, 1179-1225, (2014) · Zbl 1294.35094 [14] Dreher, J.; Runban, V.; Grauer, R., Axisymmetric flows in Hall-MHD: a tendency towards finite-time singularity formation, Phys. Scr., 72, 451-455, (2005) [15] Fan, J.; Huang, S.; Nakamura, G., Well-posedness for the axisymmetric incompressible viscous Hall-magnetohydrodynamic equations, Appl. Math. Lett., 26, 9, 963-967, (2013) · Zbl 1315.35164 [16] Fan, J.; Ozawa, T., Regularity criteria for Hall-magnetohydrodynamics and the space-time monopole equation in Lorenz gauge, Contemp. Math., 612, 81-89, (2014) · Zbl 1297.35068 [17] Triebel, H., Theory of function spaces, (1983), Birkhäuser Basel · Zbl 0546.46028 [18] Chen, Q.; Miao, C., Existence theorem and blow-up criterion of the strong solutions to the two-fluid MHD equation in \(\mathbb{R}^3\), J. Differential Equations, 239, 251-271, (2007) · Zbl 1267.76130 [19] Ogawa, T., Sharp Sobolev inequality of logarithmic type and the limiting regularity condition to the harmonic heat flow, SIAM J. Math. Anal., 34, 1318-1330, (2003) · Zbl 1036.35082 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.