Global strong solutions of a 2-D new magnetohydrodynamic system. (English) Zbl 07177874

Summary: The main objective of this paper is to study the global strong solution of the parabolic-hyperbolic incompressible magnetohydrodynamic model in the two dimensional space. Based on Agmon, Douglis, and Nirenberg’s estimates for the stationary Stokes equation and Solonnikov’s theorem on \(L^p\)-\(L^q\)-estimates for the evolution Stokes equation, it is shown that this coupled magnetohydrodynamic equations possesses a global strong solution. In addition, the uniqueness of the global strong solution is obtained.


35Q35 PDEs in connection with fluid mechanics
35D35 Strong solutions to PDEs
35B65 Smoothness and regularity of solutions to PDEs
76W05 Magnetohydrodynamics and electrohydrodynamics
35Q61 Maxwell equations
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