Exact solutions to the three-dimensional incompressible magnetohydrodynamics equations without viscosity

Junchao CHEN, Man Wai YUEN

Research output: Contribution to journalArticlespeer-review

Abstract

The incompressible magnetohydrodynamics (MHD) equations have been widely used to describe many physical systems in geophysics, astrophysics, cosmology and engineering. In this paper, we construct two types of exact global solutions with elementary functions to the three-dimensional incompressible MHD equations without viscosity. The first type of solutions is expressed by exponential functions that are nonstationary and correspond to a generalization of the well-known Arnold–Beltrami–Childress (ABC) flow for the three-dimensional MHD system. The second type of solutions has rational forms that are rotational and are similar to the ABC flow. Both types of solutions can exhibit interesting local behaviors with infinite energy. Under special parameter values, these solutions can be reduced to those of the incompressible Euler equations. Copyright © 2021 The Author(s), under exclusive licence to Springer Nature B.V.
Original languageEnglish
Pages (from-to)919-926
JournalNonlinear Dynamics
Volume106
Issue number1
Early online date14 Sep 2021
DOIs
Publication statusPublished - Sep 2021

Citation

Chen, J., & Yuen, M. (2021). Exact solutions to the three-dimensional incompressible magnetohydrodynamics equations without viscosity. Nonlinear Dynamics, 106(1), 919-926. doi: 10.1007/s11071-021-06881-7

Keywords

  • Magnetohydrodynamics equations
  • Exact solutions
  • Arnold–Beltrami–Childress flow
  • Euler equations

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