On the Splash Singularity for the free-boundary problem of the viscous and non-resistive incompressible magnetohydrodynamic equations in 3D

2023/09/18 by Guangyi Hong, Tao Luo, Hong, Guangyi +3 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2309.09747

openalex publication_date 2023/09/18 · openalex created_date 2023/09/20 · openalex updated_date 2026/07/28

Abstract

In this paper, the existence of finite-time splash singularity is proved for the free-boundary problem of the viscous and non-resistive incompressible magnetohydrodynamic (MHD) equations in ℝ³, based on a construction of a sequence of initial data alongside delicate estimates of the solutions. The result and analysis in this paper generalize those by Coutand and Shkoller in [14, Ann. Inst. H. Poincaré C Anal. Non Linéaire, 2019] from the viscous surface waves to the viscous conducting fluids with magnetic effects for which non-trivial magnetic fields may present on the free boundary. The arguments in this paper also hold for any space dimension d≥ 2.

Cited by

• Finite-Time Splash in Free Boundary Problem of 3D Neo-Hookean Elastodynamics

Related

• On Magnetic Inhibition Theory in Non-resistive Magnetohydrodynamic Fluids: Existence of Solutions in Some Classes of Large Data
• Inviscid Limit for the Free-Boundary problems of MHD Equations with or without Surface Tension
• The local characterizations of the singularity formation for the MHD equations
• On the splash singularity for the free-surface of a Navier-Stokes fluid
• Splash-squeeze singularities and analytic breakdown in ideal incompressible MHD