Global Existence for a Class of Large Solutions to Three-Dimensional Compressible Magnetohydrodynamic Equations with Vacuum

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

“…Recently, Li-Xu-Zhang [13] established the global existence and uniqueness of classical solutions to the Cauchy problem for the isentropic compressible MHD system in 3D with smooth initial data which are of small energy but possibly large oscillations and vacuum, which generalized the result for compressible Navier-Stokes equations obtained by Huang-Li-Xin [11]. Very recently, Hong-Hou-Peng-Zhu [7] improved the result in [13] to allow the initial energy large as long as the adiabatic exponent is close to 1 and ν is suitably large.…”

“…For constants q > 2 and a > 1, assume that the initial data 7) and the following compatibility condition…”

Singularity Formation of the Non-barotropic Compressible Magnetohydrodynamic Equations Without Heat Conductivity

“…There is huge literature on the studies about the theory of well-posedness of solutions to the Cauchy problem and the initial boundary value problem (IBVP) for the compressible MHD system due to the physical importance, complexity, rich phenomena, and mathematical challenges, refer to [2,[6][7][8]14,21] and references therein. However, many physical important and mathematical fundamental problems are still open due to the lack of smoothing mechanism and the strong nonlinearity.…”

Global well‐posedness of classical solutions to 3D compressible magnetohydrodynamic equations with large potential force

“…Liu established the global classical solutions if the viscosity coefficient μ is large enough. If the adiabatic exponent γ is close to 1, Hong et al obtained the global existence of classical solutions where the initial energy may be large. Considering the full compressible MHD system, for 3D cases, Hu and Wang established the existence of a global variational weak solution to the initial‐boundary value problem with large data.…”

“…The local large strong solutions to Cauchy problem and initial‐boundary‐value problem have been obtained, respectively, by Fan and Yu and Xi and Hao . Pu and Guo proved the global existence of the smooth solutions close to an equilibrium state where the initial data are in ; Xu et al proved the existence and uniqueness of a global strong solution to the system for the initial data close to a stable equilibrium state in critical Besov spaces. For 2D cases, Lu and Huang studied the local strong solutions to the Cauchy problem with vacuum and zero heat conduction.…”