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.
|Number of pages||38|
|Journal||Advances in Differential Equations|
|Publication status||Published - Jan 1 2019|
All Science Journal Classification (ASJC) codes
- Applied Mathematics