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A blow-up criterion for three-dimensional compressible magnetohydrodynamic equations with variable viscosity

Supported by Chongqing Research Program of Basic Research and Frontier Technology (No. cstc2018jcyjAX0049), the Postdoctoral Science Foundation of Chongqing (No. xm2017015), and China Postdoctoral Science Foundation (Nos. 2018T110936, 2017M610579).
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  • We are concerned with the breakdown of strong solutions to the three-dimensional compressible magnetohydrodynamic equations with density-dependent viscosity. It is shown that for the initial density away from vacuum, the strong solution exists globally if the gradient of the velocity satisfies $ \|\nabla{\bf{u}}\|_{L^{2}(0,T;L^\infty)}<\infty $. Our method relies upon the delicate energy estimates and elliptic estimates.

    Mathematics Subject Classification: 76W05, 35B65.

    Citation:

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