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A regularity criterion for 3D density-dependent MHD system with zero viscosity

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  • This paper proves a regularity criterion $\nabla u,\nabla b\in L^\infty(0,T;L^\infty)$ for 3D density-dependent MHD system with zero viscosity and positive initial density.
    Mathematics Subject Classification: 35Q30, 76D03, 76D07.


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    J. Fan, F. Li, G. Nakamura, Z. Tan, Regularity criteria for the three-dimensional magnetohydrodynamic equations. J. Diff. Equ. 256(2014) 2858-2875.


    J. Fan, Y. Zhou, Uniform local well-posedness for the density-dependent magnetohydrodynamic equations. Appl. Math. Lett. 24(11)(2011) 1945-1949.


    D. Chae, J. Lee, Local existence and blow-up criterion of the inhomogeneous Euler equations. J. Math. Fluid Mech. 5(2003) 144-165.


    T. Kato, G. Ponce, Commutator estimates and the Euler and the Navier-Stokes equations. Comm. Pure Appl. Math. 41(1988) 891-907.

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