Geodesic
Global strong solutions of a 2-D new magnetohydrodynamic system
Applications of Mathematics, Tome 65 (2020) no. 1, pp. 105-120.

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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.
DOI : 10.21136/AM.2020.0208-19
Classification : 35B65, 35D35, 35Q35, 35Q61, 76W05
Keywords: global strong solution; magnetohydrodynamics; Stokes equation; $L^p$-$L^q$-estimates 
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Liu, Ruikuan; Yang, Jiayan. Global strong solutions of a 2-D new magnetohydrodynamic system. Applications of Mathematics, Tome 65 (2020) no. 1, pp. 105-120. doi : 10.21136/AM.2020.0208-19. http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0208-19/

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