1D Model for the 3D Magnetohydrodynamics

We propose a one-dimensional (1D) model for the three-dimensional (3D) incompressible ideal magnetohydrodynamics. For this 1D model, local well-posedness is established, and a regularity criterion of the Beale–Kato–Majda type is obtained. Without the stretching effect, the model with only transport...

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Bibliographic Details
Published inJournal of nonlinear science Vol. 33; no. 5
Main Authors Dai, Mimi, Vyas, Bhakti, Zhang, Xiangxiong
Format Journal Article
LanguageEnglish
Published New York Springer US 01.10.2023
Springer Nature B.V
Subjects
Analysis
Classical Mechanics
Economic Theory/Quantitative Economics/Mathematical Methods
Magnetohydrodynamics
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical models
Mathematics
Mathematics and Statistics
One dimensional models
Singularities
Theoretical
Three dimensional models
Hilbert transform
Magnetohydrodynamics
65M70
1D simplified model
35Q35
76B03
76D03
Singularity formation
Regularity
76W05
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Summary:We propose a one-dimensional (1D) model for the three-dimensional (3D) incompressible ideal magnetohydrodynamics. For this 1D model, local well-posedness is established, and a regularity criterion of the Beale–Kato–Majda type is obtained. Without the stretching effect, the model with only transport effect is shown to have global in time strong solution. Some numerical simulations suggest that solutions of the model with certain smooth periodic initial data are not likely to develop singularities in finite time, while solutions starting from other initial data have the tendency to form singularities.
ISSN:0938-8974
1432-1467
DOI:10.1007/s00332-023-09944-8