On the Well-posedness of Magnetohydrodynamics Equations for Incompressible Electrically-Conducting Fluids

2014/01/09 by F. Lam, Lam, F.
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1401.2029

openalex publication_date 2014/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that the Cauchy problem of the equations in magnetohydrodynamics in the whole space is globally well-posed for any initial smooth and localized data. In general, the mathematical structure of solution shows that the coupled magnetic-vortical field has the characters of turbulence, if the initial data exceed certain size. In particular, if a strong magnetic force dominates the flow evolution, the current density possesses a cubic non-linearity. The solution of the non-linear problem has been constructed and has been expressed as an infinite series.

Citations

• Inertial-Range Spectrum of Hydromagnetic Turbulence
• Sur le mouvement d'un liquide visqueux emplissant l'espace
• Some mathematical questions related to the mhd equations
• Integral Invariance and Non-linearity Reduction for Proliferating Vorticity Scales in Fluid Dynamics

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• Global strong solutions to the Cauchy problem of the planar non-resistive magnetohydrodynamic equations with large initial data