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Global strong solution and exponential decay for nonhomogeneous Navier-Stokes and magnetohydrodynamic equations

Supported by National Natural Science Foundation of China (No. 11901474)

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  • The present paper concerns an initial boundary value problem of two-dimensional (2D) nonhomogeneous magnetohydrodynamic (MHD) equations with non-negative density. We establish the global existence and exponential decay of strong solutions. In particular, the initial data can be arbitrarily large. The key idea is to use a lemma due to Desjardins (Arch. Rational Mech. Anal. 137:135–158, 1997).

    Mathematics Subject Classification: 76W05;76D03.

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