Institute of Mathematics

References:
[1] S. Agmon, A. Douglis, L. Nirenberg: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II. Commun. Pure Appl. Math. 17 (1964), 35-92. DOI 10.1002/cpa.3160170104 | MR 0162050 | Zbl 0123.28706
[2] C. Amrouche, V. Girault: Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension. Czech. Math. J. 44 (1994), 109-140. MR 1257940 | Zbl 0823.35140
[3] C. Cao, J. Wu: Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion. Adv. Math. 226 (2011), 1803-1822. DOI 10.1016/j.aim.2010.08.017 | MR 2737801 | Zbl 1213.35159
[4] S. Chandrasekhar: Hydrodynamic and Hydromagnetic Stability. International Series of Monographs on Physics, Clarendon Press, Oxford (1961). MR 0128226 | Zbl 0142.44103
[5] G. Duvaut, J. L. Lions: Inéquations en thermoélasticité et magnétohydrodynamique. Arch. Ration. Mech. Anal. 46 (1972), 241-279. (In French.) DOI 10.1007/BF00250512 | MR 0346289 | Zbl 0264.73027
[6] M. Geissert, M. Hess, M. Hieber, C. Schwarz, K. Stavrakidis: Maximal $L^p$-$L^q$-estimates for the Stokes equation: a short proof of Solonnikov's theorem. J. Math. Fluid Mech. 12 (2010), 47-60. DOI 10.1007/s00021-008-0275-0 | MR 2602914 | Zbl 1261.35120
[7] C. He, Z. Xin: On the regularity of weak solutions to the magnetohydrodynamic equations. J. Differ. Equations 213 (2005), 235-254. DOI 10.1016/j.jde.2004.07.002 | MR 2142366 | Zbl 1072.35154
[8] X. Huang, Y. Wang: Global strong solution to the 2D nonhomogeneous incompressible MHD system. J. Differ. Equations 254 (2013), 511-527. DOI 10.1016/j.jde.2012.08.029 | MR 2990041 | Zbl 1253.35121
[9] Q. Jiu, D. Niu, J. Wu, X. Xu, H. Yu: The 2D magnetohydrodynamic equations with magnetic diffusion. Nonlinearity 28 (2015), 3935-3955. DOI 10.1088/0951-7715/28/11/3935 | MR 3424899 | Zbl 1328.76076
[10] R. Liu, Q. Wang: $S^1$ attractor bifurcation analysis for an electrically conducting fluid flow between two rotating cylinders. Physica D 392 (2019), 17-33. DOI 10.1016/j.physd.2019.03.001 | MR 3928313
[11] R. Liu, J. Yang: Magneto-hydrodynamical model for plasma. Z. Angew. Math. Phys. 68 (2017), Article number 114, 15 pages. DOI 10.1007/s00033-017-0861-1 | MR 3704274 | Zbl 1386.76191
[12] T. Ma: Theory and Method of Partial Differential Equation. Science Press, Beijing (2011). (In Chinese.)
[13] T. Ma, S. Wang: Phase Transition Dynamics. Springer, New York (2014). DOI 10.1007/978-1-4614-8963-4 | MR 3154868 | Zbl 1285.82004
[14] N. Masmoudi: Global well posedness for the Maxwell-Navier-Stokes system in 2D. J. Math. Pures Appl. (9) 93 (2010), 559-571. DOI 10.1016/j.matpur.2009.08.007 | MR 2651981 | Zbl 1192.35133
[15] D. Regmi: Global weak solutions for the two-dimensional magnetohydrodynamic equations with partial dissipation and diffusion. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 144 (2016), 157-164. DOI 10.1016/j.na.2016.07.002 | MR 3534099 | Zbl 1348.35196
[16] X. Ren, J. Wu, Z. Xiang, Z. Zhang: Global existence and decay of smooth solution for the 2-D MHD equations without magnetic diffusion. J. Funct. Anal. 267 (2014), 503-541. DOI 10.1016/j.jfa.2014.04.020 | MR 3210038 | Zbl 1295.35104
[17] T. Sengul, S. Wang: Pattern formation and dynamic transition for magnetohydrodynamic convection. Commun. Pure Appl. Anal. 13 (2014), 2609-2639. DOI 10.3934/cpaa.2014.13.2609 | MR 3248406 | Zbl 1305.76130
[18] M. Sermange, R. Temam: Some mathematical questions related to the MHD equations. Commun. Pure Appl. Math. 36 (1983), 635-664. DOI 10.1002/cpa.3160360506 | MR 0716200 | Zbl 0524.76099
[19] V. A. Solonnikov: Estimates for solutions of nonstationary Navier-Stokes equations. J. Sov. Math. 8 (1977), 467-529. DOI 10.1007/BF01084616 | Zbl 0404.35081
[20] R. Temam: Navier-Stokes Equations. Theory and Numerical Analysis. American Mathematical Society, Providence (2001). DOI 10.1090/chel/343 | MR 1846644 | Zbl 0981.35001
[21] V. Vialov: On the regularity of weak solutions to the MHD system near the boundary. J. Math. Fluid Mech. 16 (2014), 745-769. DOI 10.1007/s00021-014-0184-3 | MR 3267547 | Zbl 1308.35228
[22] Q. Wang: Stability and bifurcation of a viscous incompressible plasma fluid contained between two concentric rotating cylinders. Discrete Contin. Dyn. Syst., Ser. B. 19 (2014), 543-563. DOI 10.3934/dcdsb.2014.19.543 | MR 3170198 | Zbl 1292.76078
[23] T. Wang: A regularity criterion of strong solutions to the 2D compressible magnetohydrodynamic equations. Nonlinear Anal., Real World Appl. 31 (2016), 100-118. DOI 10.1016/j.nonrwa.2016.01.011 | MR 3490834 | Zbl 1338.35088
[24] J. Wu: Generalized MHD equations. J. Differ. Equations 195 (2003), 284-312. DOI 10.1016/j.jde.2003.07.007 | MR 2016814 | Zbl 1057.35040
[25] K. Yamazaki: Global regularity of $N$-dimensional generalized MHD system with anisotropic dissipation and diffusion. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 122 (2015), 176-191. DOI 10.1016/j.na.2015.04.006 | MR 3348070 | Zbl 1319.35201
[26] X. Zhong: Global strong solutions for 3D viscous incompressible heat conducting magnetohydrodynamic flows with non-negative density. J. Math. Anal. Appl. 446 (2017), 707-729. DOI 10.1016/j.jmaa.2016.09.012 | MR 3554752 | Zbl 1352.35133