Global existence and convergence rates of smooth solutions for the full compressible MHD equations

On strong solutions to the compressible Hall-magnetohydrodynamic system

“…When the Hall effect term curl  curl b×b ρ  is neglected, the system (1.1)-(1.6) reduces to the well-known compressible isentropic MHD system, which has received many studies [10][11][12][13][14][15][16][17][18][19]. The local strong solution was proved by Fan-Yu [10].…”

“…The low Mach number limit problem was studied by Hu-Wang [15] and Jiang-Ju-Li [16]. Li-Yu [17], Chen-Tan [18], and Pu-Guo [19] showed the time decay of smooth solutions.…”

Strong solutions to 3D compressible magnetohydrodynamic equations with Navier‐slip condition

“…Nevertheless, this has been well understood to be successful on the MHD system in the case of no‐slip conditions and the whole space , such as strong solution of global existence for sufficiently small initial data and local existence for arbitrary data. More precisely, Fan and Yu obtained local strong solutions to the compressible MHD with large initial data; Pu and Guo proved the global existence of smooth solutions to the full MHD in three dimensions when the initial data are small perturbations of a given constant state; Li et al . showed the global well‐posedness of classical solution for regular initial data with small energy.…”

Long‐time behavior of solution for the compressible Navier‐Stokes‐Maxwell equations in

“…Motivated by the work of Guo and Wang, Tan and Wang established the optimal time decay rates for the higher‐order spatial derivatives of solutions if the initial perturbation belongs to . For the full compressible MHD Equations , Pu and Guo established the small global classical solution and the time decay rates, which has been improved by Gao et al recently.…”