Strong solutions to the Cauchy problem of two-dimensional non-barotropic non-resistive magnetohydrodynamic equations with zero heat conduction

Stability near equilibrium to the full compressible magnetohydrodynamic equations

“…Due to their broad physical applications, complexity, rich phenomena and mathematical challenges, the MHD equations have recently attracted considerable interests. See [1], [2], [4], [6]- [13], [15], [16], [18]- [52], [54]- [56] and the references therein. In particular, taking the temperature into consideration, the problem becomes more complicated.…”

Local existence of compressible MHD equations without initial compatibility conditions

“…Compared with the compressible Navier-Stokes equations, the study of the well-posedness of the compressible MHD equations is quite complex due to the strong coupling and interaction between fluid motion and magnetic field. Effective methods need to be found to handle strong coupling and strong nonlinearity terms, whose unique characteristics make analytical research a huge challenge but also provide new opportunities 8,9,10 . There has been many works on the mathematical studies the compressible MHD equations in fluid dynamics.…”

Singularity formation to the 2D Cauchy problem of nonbarotropic magnetohydrodynamic equations without heat conductivity

“…For more background, we refer to [1, 17]. Due to the profound physical background and important mathematical significance, a great deal of attention has been focused on studying well‐posedness of solutions to the compressible MHD system, both from a pure mathematical point of view and for concrete applications, please refer to [5, 9–11, 15, 20, 23, 30, 31] and references therein. In 1983, Kawashima [14] obtained the global existence and uniqueness of classical solutions when the initial data are close to a nonvacuum equilibrium in H 3 ‐norm.…”