Well-posedness and large time behavior of solutions for the electron inertial Hall-MHD system

Yasuhide Fukumoto, Xiaopeng Zhao

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1 Citation (Scopus)

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 0H˙ 1/2 +∥B 0H˙ 1/2 +∥∇B 0H˙ 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 languageEnglish
Pages (from-to)31-68
Number of pages38
JournalAdvances in Differential Equations
Volume24
Issue number1-2
Publication statusPublished - Jan 1 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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