Estimation of decay rates to large-solutions of 3D compressible magnetohydrodynamic system

Abstract

The aim of this paper is to get an estimation of decay rates to first-order and second-order derivatives of space for large-solutions to 3D compressible magnetohydrodynamic system. While the condition (σ0 − 1, u0, Q0) ∈ L1 ∩ H2 is satisfied via a classical energy method and Fourier splitting method, first-order and second-order derivatives of space for large-solutions tending to 0 by L2-rate (1+t)−54 are shown. It is a necessary supplement to the result of Gao, Wei, and Yao [Appl. Math. Lett. 102, 106100 (2020)] in which they only obtained an estimation of decay rates to magnetic fields. Meanwhile, compared with the work of Gao, Wei, and Yao [Physica D 406, 132506 (2020)], we find that the appearance of magnetic fields does not have any bad effect on the estimation of decay rates to both the velocity field and density.