On the Existence and Temporal Asymptotics of Solutions for the Two and Half Dimensional Hall MHD

Hantaek Bae, Kyungkeun Kang

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we deal with the 212 dimensional Hall MHD by taking the velocity field u and the magnetic field B of the form u(t, x, y) = (∇ ϕ(t, x, y) , W(t, x, y)) and B(t, x, y) = (∇ ψ(t, x, y) , Z(t, x, y)). We begin with the Hall equations (without the effect of the fluid part). In this case, we provide several results such as the long time behavior of weak solutions, weak-strong uniqueness, the existence of local and global in time strong solutions, decay rates of (ψ, Z) , the asymptotic profiles of (ψ, Z) , and the perturbation around harmonic functions. In the presence of the fluid field, the results, by comparison, fall short of the previous ones in the absence of the fluid part and we show the existence of local and global in time strong solutions.

Original languageEnglish
Article number24
JournalJournal of Mathematical Fluid Mechanics
Volume25
Issue number2
DOIs
Publication statusPublished - 2023 May

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics

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