Stability of perturbations near a background magnetic field of the 2D incompressible MHD equations with mixed partial dissipation

Abidi, 2017, On the global solution of 3D MHD system with initial data near equilibrium, Commun. Pure Appl. Math., 70, 1509, 10.1002/cpa.21645 Alemany, 1979, Influence of an external magnetic field on homogeneous MHD turbulence, J. Méc., 18, 277 Alexakis, 2011, Two-dimensional behavior of three-dimensional magnetohydrodynamic flow with a strong guiding field, Phys. Rev. E, 84, 10.1103/PhysRevE.84.056330 Alfvén, 1942, Existence of electromagnetic-hydrodynamic waves, Nature, 150, 405, 10.1038/150405d0 Bardos, 1988, Longtime dynamics of a conductive fluid in the presence of a strong magnetic field, Trans. Am. Math. Soc., 305, 175, 10.1090/S0002-9947-1988-0920153-5 Cai, 2018, Global well-posedness of the incompressible magnetohydrodynamics, Arch. Ration. Mech. Anal., 228, 969, 10.1007/s00205-017-1210-4 Cao, 2011, Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion, Adv. Math., 226, 1803, 10.1016/j.aim.2010.08.017 Davidson, 2001 Deng, 2018, Large time behavior of solutions to 3-D MHD system with initial data near equilibrium, Arch. Ration. Mech. Anal., 230, 1017, 10.1007/s00205-018-1265-x Denisov, 2015, Double-exponential growth of the vorticity gradient for the two-dimensional Euler equation, Proc. Am. Math. Soc., 143, 1199, 10.1090/S0002-9939-2014-12286-6 Dong, 2019, Global regularity for the 2D MHD equations with partial hyperresistivity, Int. Math. Res. Not., 2019, 4261, 10.1093/imrn/rnx240 Duvaut, 1972, Inequations en thermoelasticite et magnetohydrodynamique, Arch. Ration. Mech. Anal., 46, 241, 10.1007/BF00250512 Gallet, 2009, Influence of an external magnetic field on forced turbulence in a swirling flow of liquid metal, Phys. Fluids, 21, 10.1063/1.3194304 Gallet, 2015, Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field, J. Fluid Mech., 773, 154, 10.1017/jfm.2015.232 He, 2018, On global dynamics of three dimensional magnetohydrodynamics: nonlinear stability of Alfvén waves, Ann. PDE, 4, 10.1007/s40818-017-0041-9 Hu Hu Kiselev, 2014, Small scale creation for solutions of the incompressible two-dimensional Euler equation, Ann. Math., 180, 1205, 10.4007/annals.2014.180.3.9 Laudau, 1984 Lin, 2015, Global small solutions to 2-D incompressible MHD system, J. Differ. Equ., 259, 5440, 10.1016/j.jde.2015.06.034 Pan, 2018, Global classical solutions of three dimensional viscous MHD system without magnetic diffusion on periodic boxes, Arch. Ration. Mech. Anal., 227, 637, 10.1007/s00205-017-1170-8 Ren, 2014, Global existence and decay of smooth solution for the 2-D MHD equations without magnetic diffusion, J. Funct. Anal., 267, 503, 10.1016/j.jfa.2014.04.020 Ren, 2016, Global well-posedness for the 2D MHD equations without magnetic diffusion in a strip domain, Nonlinearity, 29, 1257, 10.1088/0951-7715/29/4/1257 Schonbek, 1985, L2 decay for weak solutions of the Navier-Stokes equations, Arch. Ration. Mech. Anal., 88, 209, 10.1007/BF00752111 Schonbek, 1996, On the decay of higher-order norms of the solutions of Navier-Stokes equations, Proc. R. Soc. Edinb., Sect. A, 126, 677, 10.1017/S0308210500022976 Sermange, 1983, Some mathematical questions related to the MHD equations, Commun. Pure Appl. Math., 36, 635, 10.1002/cpa.3160360506 Tan, 2018, Global well-posedness of an initial-boundary value problem for viscous non-resistive MHD systems, SIAM J. Math. Anal., 50, 1432, 10.1137/16M1088156 Tao, 2006, Nonlinear Dispersive Equations: Local and Global Analysis Wei, 2017, Global well-posedness of the MHD equations in a homogeneous magnetic field, Anal. PDE, 10, 1361, 10.2140/apde.2017.10.1361 Wu, 2018, The 2D magnetohydrodynamic equations with partial or fractional dissipation, 283 Wu, 2017, Global small solutions to the compressible 2D magnetohydrodynamic system without magnetic diffusion, Adv. Math., 310, 759, 10.1016/j.aim.2017.02.013 Wu, 2015, Global small solution to the 2D MHD system with a velocity damping term, SIAM J. Math. Anal., 47, 2630, 10.1137/140985445 J. Wu, Y. Zhu, Global solutions of 3D incompressible MHD system with mixed partial dissipation and magnetic diffusion near an equilibrium, Submitted for publication. Zhang Zhang, 2016, Global solutions to the 2D viscous, non-resistive MHD system with large background magnetic field, J. Differ. Equ., 260, 5450, 10.1016/j.jde.2015.12.005 Zhou, 2018, Global classical solutions of 2D MHD system with only magnetic diffusion on periodic domain, J. Math. Phys., 59, 10.1063/1.5018641 Zlatos, 2015, Exponential growth of the vorticity gradient for the Euler equation on the torus, Adv. Math., 268, 396, 10.1016/j.aim.2014.08.012