A STABILITY PROBLEM FOR THE 3D MAGNETOHYDRODYNAMIC EQUATIONS NEAR EQUILIBRIUM

doi:10.1007/s10473-021-0405-9

Abstract

Abstract: This paper is concerned with a stability problem on perturbations near a physically important steady state solution of the 3D MHD system. We obtain three major results. The first assesses the existence of global solutions with small initial data. Second, we derive the temporal decay estimate of the solution in the L²-norm, where to prove the result, we need to overcome the difficulty caused by the presence of linear terms from perturbation. Finally, the decay rate in L² space for higher order derivatives of the solution is established.

Key words: Background magnetic field, MHD equations with perturbation, stability, decay rate

CLC Number:

35Q35

Xueli KE, Baoquan YUAN, Yaomin XIAO. A STABILITY PROBLEM FOR THE 3D MAGNETOHYDRODYNAMIC EQUATIONS NEAR EQUILIBRIUM[J].Acta mathematica scientia,Series B, 2021, 41(4): 1107-1118.

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