Global well-posedness for the incompressible Hall-magnetohydrodynamic system in critical Fourier–Besov spaces

Ryosuke Nakasato*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We investigate the initial value problem for the incompressible magnetohydrodynamic system with the Hall-effect in the whole space R3. In this paper, we focus on a solution as a perturbation from a constant equilibrium state (0 , B¯) , where 0 ∈ R3 is the zero velocity and B¯ ∈ R3 is a constant magnetic field. Our goal is to establish the existence of a global-in-time solution in Lp-type critical Fourier–Besov spaces. In order to prove our results, we establish various type product estimates in space-time mixed spaces and smoothing estimates for the solution of the linear equation, which has a non-symmetric diffusion derived from the Hall-term. Our results hold in the case of small initial data. However, the result can cover initial velocity fields whose high frequency part is highly oscillating.

Original languageEnglish
Article number20
JournalJournal of Evolution Equations
Volume22
Issue number1
DOIs
Publication statusPublished - 2022 Mar
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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