Asymptotic Stability of Couette Flow in a Strong Uniform Magnetic Field for the Euler-MHD System

Weiren Zhao, Ruizhao Zi

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we prove the asymptotic stability of Couette flow in a strong uniform magnetic field for the Euler-MHD system, when the perturbations are in Gevrey-1s, (12<s≦1) and of size smaller than the resistivity coefficient μ. More precisely, we prove that the μ-13-amplification of the perturbed vorticity, namely, the size of the vorticity grows from ‖ωin‖Gλ0≲μ to ‖ω‖Gλ≲μ23; the polynomial decay of the perturbed current density, namely, j≠L2≲c0⟨t⟩2minμ-13,⟨t⟩; and the damping for the perturbed velocity and magnetic field, namely, (Formula presented.) We also confirm that the strong uniform magnetic field stabilizes the Euler-MHD system near Couette flow.

Original languageEnglish (US)
Article number47
JournalArchive for Rational Mechanics and Analysis
Volume248
Issue number3
DOIs
StatePublished - Jun 2024

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

Fingerprint

Dive into the research topics of 'Asymptotic Stability of Couette Flow in a Strong Uniform Magnetic Field for the Euler-MHD System'. Together they form a unique fingerprint.

Cite this