### Abstract

In this paper, the properties of weak and strong solutions for the Hall-magnetohydrodynamic system augmented by the effect of elec- tron inertia are studied. First, we establish the existence and uniqueness of local-in-time strong solutions; Then, we prove the existence of global strong solutions under the condition that ∥u _{0} ∥ _{H˙ 1/2} +∥B _{0} ∥ _{H˙ 1/2} +∥∇B _{0} ∥ _{H˙ 1/2} is sufficiently small. Moreover, by applying a cut-off function and gen- eralized energy inequality, we show that the weak solution of electron inertia Hall-MHD system approaches zero as the time t → ∞. Finally, the algebraic decay rate of the weak solution of electron inertia Hall- MHD system is established by using Fourier splitting method and the properties of decay character.

Original language | English |
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Pages (from-to) | 31-68 |

Number of pages | 38 |

Journal | Advances in Differential Equations |

Volume | 24 |

Issue number | 1-2 |

Publication status | Published - Jan 1 2019 |

### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

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## Cite this

*Advances in Differential Equations*,

*24*(1-2), 31-68.