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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.

MSC:

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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