### 抜粋

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.

元の言語 | 英語 |
---|---|

ページ（範囲） | 31-68 |

ページ数 | 38 |

ジャーナル | Advances in Differential Equations |

巻 | 24 |

発行部数 | 1-2 |

出版物ステータス | 出版済み - 1 1 2019 |

### フィンガープリント

### All Science Journal Classification (ASJC) codes

- Analysis
- Applied Mathematics

### これを引用

*Advances in Differential Equations*,

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