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Global Existence and Optimal Decay Rate of the Compressible Magnetohydrodynamic Equation with Potential Force

  • Mathematics
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Wuhan University Journal of Natural Sciences

Abstract

In this paper, we consider the three dimensional compressible viscous magnetohydrodynamic equations (MHD) with the external potential force. We first derive the corresponding non-constant stationary solutions. Next, we show global wellposedness of the initial value problem for the three dimensional compressible viscous magnetohydrodynamic equations, provided that the initial data is close to the stationary solution. Finally, based on the elaborate energy estimates for the nonlinear system and Lp - Lq decay estimates of the linearized equation, we show the optimal convergence rates of the solution in Lq-norm with 2⩽q⩽6 and its first derivative in L2-norm when the initial perturbation is bounded in Lp-norm with 1⩽ p<6 5.

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Authors and Affiliations

  1. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

    Lin Ye & Yeping Li

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  1. Lin Ye
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  2. Yeping Li
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Correspondence to Yeping Li.

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Foundation item: Supported by the National Natural Science Foundation of China (11671134)

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Ye, L., Li, Y. Global Existence and Optimal Decay Rate of the Compressible Magnetohydrodynamic Equation with Potential Force. Wuhan Univ. J. Nat. Sci. 23, 309–317 (2018). https://doi.org/10.1007/s11859-018-1327-9

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  • DOI: https://doi.org/10.1007/s11859-018-1327-9

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