Incompressible limit of full compressible magnetohydrodynamic equations with well-prepared data in 3-D bounded domains

Low Mach number limit of the full compressible Hall-MHD system

“…However, the only different term between our system and that in [2] is the Hall term. On the other hand, we will only use the formulation of M ptq, which is same as that in [2] in our estimates. For example, we mainly use sup…”

“…The novelty of our paper lies in that the system has the Hall term with strong nonlinearity and therefore the difference between our paper and the references [2,7,19,20] is that we will bound some new terms I i pi " 1,¨¨¨, 6q coming from the Hall term.…”

“…When the Hall effect term rot´r ot bˆb ρ¯i s neglected, the system (1)-(5) reduces to the well-known full compressible MHD system, which has received many studies [2,8,13,14,16,17,19]. The local strong solution was obtained by Fan-Yu [13].…”

“…The global weak solutions was obtained by Fan-Yu [14], Ducomet-Feireisl [8] and Hu-Wang [16] respectively. The low Mach number limit problem was studied by Jiang-Ju-Li [18] in T 3 for well-prepared initial data, Jiang-Ju-Li-Xin [19] in R 3 for ill-prepared initial data, and Cui-Ou-Ren [2] in a bounded domain for well-prepared initial data.…”

Local well‐posedness and blow‐up criterion for a compressible Navier‐Stokes‐P1 approximate model arising in radiation hydrodynamics

“…It follows from that []: and thus the proof of existence is complete by taking and the standard compactness principle. The uniqueness part can be shown by the very similar calculations as that in [], and thus we omit the details here.…”