2025/12/17 by Xu, Lin, Zhong, Xin
Mathematics · Engineering · #Navier-Stokes equation solutions #Gas Dynamics and Kinetic Theory #Computational Fluid Dynamics and Aerodynamics
paper · doi:10.48550/arxiv.2512.15021
We consider the Cauchy problem of the non-isentropic compressible magnetohydrodynamic equations in ℝ3 with far-field vacuum. By deriving delicate energy estimates and exploiting the intrinsic structure of the system, we establish the global existence and uniqueness of strong solutions provided that the scaling-invariant quantity (1+ρ+\tfrac1ρ) [‖ρ0‖L3+ ( ρ2+ρ)( ‖ √ρ0u0‖L22+‖ b0‖L22) ] [‖∇ u0‖L22+(ρ+1)‖√ρ0 θ0‖L22+‖ ∇ b0‖L22+‖ b0‖L44 ] is sufficiently small, where ρ denotes the essential supremum of the initial density. Our result may be regarded as an improved version compared with that of Liu and the second author (J. Differential Equations 336 (2022), pp. 456--478) in the sense that an artificial condition 3μ>λ on the viscosity coefficients is removed. In particular, we provide a new scaling-invariant quantity regarding the initial data.