Existence of strong solutions and low Mach number limit for boundary value problems of steady compressible magnetohydrodynamic equations with large external forces

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This research focuses on proving the existence of strong solutions for boundary value problems in steady compressible magnetohydrodynamic equations with large external forces and exploring the low Mach number limit.
Proved existence of strong solutions in bounded domains for steady compressible magnetohydrodynamics
Established convergence of strong solutions to incompressible magnetohydrodynamics as Mach number approaches zero
Decomposed equations into systems of large and small external forces
Developed uniform a priori estimates on Mach number for strong solutions
Demonstrated existence of strong solutions under specific constraints
Validated convergence of solutions as Mach number decreases
Showed that fluid velocity and temperature adhere to Dirichlet boundary conditions
Confirmed magnetic fields comply with complete conductivity boundary conditions

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Demonstrates strong solution existence in compressible magnetohydrodynamic equations, indicating stability under large external forces.

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Dou et al. (2026) studied this question.

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